Shock solution for quasilinear singularly perturbed Robin problem
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The shock solution for the quasilinear singularly perturbed Robin problem is considered. Under suitable conditions and using the theory of differential inequalities the existence and asymptotic behavior of the shock solution for the original boundary value problems are studied.
On a quasilinear elliptic eigenvalue problem with constraint
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.
Regularity problem for quasilinear elliptic and parabolic systems
Koshelev, Alexander
1995-01-01
The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described. The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.
QUASILINEAR ELLIPTIC BOUNDARY VALUE PROBLEMS WITH DISCONTINUOUS NONLINEARITIES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper we shall consider a discontinuous nonlinear nonmonotone elliptic boundary value problem, i.e. a quasilinear elliptic hemivariational inequality. This kind of problems is strongly motivated by various problems in mechanics. By use of the notion of the generalized gradient of Clarke and the theory of pseudomonotone operators, we will prove the existence of solutions.
A Robin Problem for Quasi-linear System
Institute of Scientific and Technical Information of China (English)
0UYANGCheng
2004-01-01
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.
Shear dynamo problem: Quasilinear kinematic theory.
Sridhar, S; Subramanian, Kandaswamy
2009-04-01
Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is nonperturbative in the shear strength. We derive the integrodifferential equation for the evolution of the mean magnetic field by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For nonhelical turbulence the time evolution of the cross-shear components of the mean field does not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence the shear-current assisted dynamo is essentially absent, although large-scale nonhelical dynamo action is not ruled out.
A note on quasilinear elliptic eigenvalue problems
Directory of Open Access Journals (Sweden)
Gianni Arioli
1999-11-01
Full Text Available We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.
CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS WITH CHARACTERISTICS WITH CONSTANT MULTIPLICITY
Institute of Scientific and Technical Information of China (English)
Wang Libin
2004-01-01
For quasilinear hyperbolic systems with characteristics of constant multiplicity, suppose that characteristics of constant multiplicity(＞1) are linearly degenerate, by means of generalized normalized coordinates we get the global existence and the blow-up phenomenon of the C1 solution to the Cauchy problem under an additional hypothesis.
POINTWISE ESTIMATES OF SOLUTIONS TO CAUCHY PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
WANG WEIKE; YANG XIONGFENG
2003-01-01
This paper considers the pointwise estimate of the solutions to Cauchy problem for quasilin-ear hyperbolic systems, which bases on the existence of the solutions by using the fundamentalsolutions. It gives a sharp pointwise estimates of the solutions on domain under consideration.Specially, the estimate is precise near each characteristic direction.
Cauchy Problem for Quasilinear Hyperbolic Systems with Higher Order Dissipative Terms
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Wei-guo Zhang
2003-01-01
In this paper, the author studies the global existence, singularities and life span of smooth solutions of the Cauchy problem for a class of quasilinear hyperbolic systems with higher order dissipative terms and gives their applications to nonlinear wave equations with higher order dissipative terms.
Quasilinear Robin Problem with Boundary Perturbation%具有边界摄动的拟线性Robin问题
Institute of Scientific and Technical Information of China (English)
陈雪东
2006-01-01
A class of quasilinear Robin problems with boundary perturbation are considered.Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
[1]Oleinik, O. A., Samokhin,V. N., Mathematical Models in Boundary Layer Theorem, Boca Raton; Chapman and Hall/CRC, 1999.[2]Volpert, A.I., Hudjaev, S.I., On the problem for quasilinear degenerate parabolic equations of second order(Russian), Mat. Sb., 1967, 3: 374-396.[3]Zhao, J., Uniqueness of solutions of quasilinear degenerate parabolic equations, Northeastern Math. J., 1985,1(2): 153-165.[4]Wu, Z., Yin, J., Some properties of functions in BVx and their applications to the uniqueness of solutions for degenerate quasilinear parabolic equations, Northeastern Math. J., 1989,5(4): 395-422.[5]Brezis, H., Crandall, M.G., Uniqueness of solutions of the initial value problem for ut- △ψ(u) = 0, J.Math. Pures et Appl., 1979, 58: 153-163.[6]Kruzkov, S.N., First order quasilinear equations in several independent varaiables, Math. USSR-Sb., 1970, 10:217-243.[7]Cockburn, B., Gripenberg, G., Continious dependence on the nonlinearities of solutions of degenerate parabolic equations, J. Diff. Equatiaons, 1999, 151: 231-251.[8]Volpert, A.I., BV space and quasilinear equations, Mat. Sb., 1967, 73: 255-302.[9]Volpert, A.I., Hudjave, S.I., Analysis of class of discontinuous functions and the equations of mathematical physics (Russian), Izda. Nauka Moskwa, 1975.[10]Evans, L.C., Weak convergence methods for nonlinear partial differential equations, Conference Board of the Mathematical Sciences, Regional Conferences Series in Mathematics Number 74, 1998.[11]Wu, Z., Zhao, J., Yin, J., et al., Nonlinear Diffusion Equations, Singapore: Word Scientific, 2001.
Solvability of a class of second-order quasilinear boundary value problems
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Qing-liu YAO
2009-01-01
The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution ff the integration of the limit growth function has an appropriate value.
Porosity of Free Boundaries in the Obstacle Problem for Quasilinear Elliptic Equations
Indian Academy of Sciences (India)
Jun Zheng; Zhihua Zhang; Peihao Zhao
2013-08-01
In this paper, we establish growth rate of solutions near free boundaries in the identical zero obstacle problem for quasilinear elliptic equations. As a result, we obtain porosity of free boundaries, which is naturally an extension of the previous works by Karp et al. (J. Diff. Equ. 164 (2000) 110–117) for -Laplacian equations, and by Zheng and Zhang (J. Shaanxi Normal Univ. 40(2) (2012) 11–13, 18) for -Laplacian type equations.
Directory of Open Access Journals (Sweden)
A. K. Pani
1987-01-01
Full Text Available Optimal error estimates in L2, H1 and H2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by an H1-Galerkin procedure.
QUASILINEAR ELLIPTIC PROBLEMS WITH CRITICAL EXPONENT AND HARDY TERM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
This paper is concerned with a p-Laplacian elliptic problem with critical Sobolev-Hardy exponent and Hardy term. By variational methods and genus theory, we guarantee that this problem has at least one positive solution and admits many solutions with negative energy under sufficient conditions.
A FEM-BEM FORMULATION FOR AN EXTERIOR QUASILINEAR ELLIPTIC PROBLEM IN THE PLANE
Institute of Scientific and Technical Information of China (English)
Dongjie Liu; Dehao Yu
2008-01-01
In this paper, the finite element method and the boundary element method are combined to solve numerically an exterior quasilinear elliptic problem. Based on an appropriate transformation and the Fourier series expansion, the exact qnasilinear artificial boundary conditions and a series of the corresponding approximations for the given problem are presented. Then the original problem is reduced into an equivalent problem defined in a bounded computational domain. We provide error estimate for the Galerkin method. Numerical results are presented to illustrate the theoretical results.
Convergence of an adaptive Ka\\v{c}anov FEM for quasi-linear problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2010-01-01
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is thus \\emph{inexact} because we do not solve the discrete nonlinear problems exactly, but rather perform one iteration of a fixed point method (Ka\\v{c}anov), using the approximation of the previous mesh as an initial guess. The convergence of the method is prov...
A multiplicity result for a class of quasilinear elliptic and parabolic problems
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M. R. Grossinho
1997-04-01
Full Text Available We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive of the nonlinearity at the right-hand side oscillates at infinity. The proof is based on the construction of upper and lower solutions, which are obtained as solutions of suitable comparison equations. This method allows the introduction of conditions on the potential for the study of parabolic problems, as well as to treat simultaneously the singular and the degenerate case.
PERIODIC BOUNDARY VALUE PROBLEM OF QUASILINEAR SYSTEM%拟线性系统周期边值问题
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The existence and uniqueness results about quasilinear periodic boundary value problems are established by using the global inverse function theorem and the result about the existence and uniquencess of periodic solutions for the periodic boundary value problem of nonhomogeneous linear periodic system.
Institute of Scientific and Technical Information of China (English)
周毓麟; 沈隆钧; 袁光伟
1997-01-01
More work is done to study the explicit, weak and strong implicit difference solution for the first boundary problem of quasilinear parabolic system:where u, , and f are m-dimensional vector valued functions, A is an m × m positively definite matrix, and ut = For this problem, the convergence of iteration for the general difference schemes is proved.
Institute of Scientific and Technical Information of China (English)
GUO Fei
2007-01-01
In this paper we study the mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems in the domain D={(t,x)| t≥O,x≥O}.Under the assumption that the source term satisfies the matching condition,a sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.
L{sup P}-posteriori error analysis of mixed methods for linear and quasilinear elliptic problems
Energy Technology Data Exchange (ETDEWEB)
Chen, Z. [Texas A& M Univ., College Station, TX (United States)
1995-12-31
We consider mixed finite element methods for the approximation of linear and quasilinear second-order elliptic problems. A class of postprocessing methods for improving mixed finite element solutions is analyzed. In particular, error estimates in L{sup p}, 1{<=}p{<=}{infinity}, are given. These postprocessing methods are applicable to an the existing mixed methods, and can be easily implemented. Furthermore, they are local and thus fully parallelizable.
Arkhipova, A. A.
2017-03-01
The Venttsel' problem in the model statement for quasilinear parabolic systems of equations with nondiagonal principal matrices is considered. It is only assumed that the principal matrices and the boundary condition are bounded with respect to the time variable. The partial smoothness of the weak solutions (Hölder continuity on a set of full measure up to the surface on which the Venttsel' condition is defined) is proved. The proof uses the A( t)-caloric approximation method, which was also used in [1] to investigate the regularity of the solution to the corresponding linear problem.
Eigenvalue problems for a quasilinear elliptic equation on ℝN
Directory of Open Access Journals (Sweden)
Marilena N. Poulou
2005-01-01
Full Text Available We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation −Δpu=λg(x|u|p−2u, x∈ℝN, lim|x|→+∞u(x=0, where Δpu=div(|∇u|p−2∇u is the p-Laplacian operator and the weight function g(x, being bounded, changes sign and is negative and away from zero at infinity.
Institute of Scientific and Technical Information of China (English)
2000-01-01
This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.
A Robin Problem for Quasi-linear System%关于拟线性系统的一个Robin问题
Institute of Scientific and Technical Information of China (English)
欧阳成
2004-01-01
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this paper, we consider the Cauchy problem with initial data given on a semi-bounded axis for inhomogeneous quasilinear hyperbolic systems. Under the assumption that the rightmost (resp. leftmost) eigenvalue is weakly linearly degenerate and the inhomogeneous term satisfies the corresponding matching condition, we obtain the global existence and uniqueness of C1 solution with small and decaying initial data.
DETERMINISTIC HOMOGENIZATION OF QUASILINEAR DAMPED HYPERBOLIC EQUATIONS
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Gabriel Nguetseng; Hubert Nnang; Nils Svanstedt
2011-01-01
Deterministic homogenization is studied for quasilinear monotone hyperbolic problems with a linear damping term.It is shown by the sigma-convergence method that the sequence of solutions to a class of multi-scale highly oscillatory hyperbolic problems converges to the solution to a homogenized quasilinear hyperbolic problem.
Institute of Scientific and Technical Information of China (English)
周毓麟; 沈隆钧; 袁光伟
1996-01-01
The explicit, weak and strong implicit difference solution for the first boundary problem ofquasilinear parabolic system is considered:where u,, and f are m-dimensional vector valued functions, A is an m x m positively definite matrix, andFor this problem, the absolute and relative stability for the general difference schemes is justifiedin the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problems.
Monotone Iterative Method for Set-valued Quasilinear Elliptic Boundary Value Problems
Institute of Scientific and Technical Information of China (English)
SUN Le-lin; XU Di-hong; CHENG Jian; Li Rong-hua
2001-01-01
@@1. Problem and Assumptions This paper deals with the solutions of the following differential inclusion problem: Au ∈f(x,u), x ∈ Ω; (1) u =0, x∈ Ω, whereAu(x)=Ω RN is a bounded domain with piecewise Lipschitz boundary Ω , Du = (D1 u, D2 u,…,DNu), Diu = , i = 1,2,…, N, and f: Ω × R→2R is a set-valued unction.
Two-scale meshes in quasilinear discretized problems of computational mechanics
Jarošová, P.; Vala, J.
2016-06-01
Some problems of continuum mechanics, as the analysis of crack formation in the cohesive zone modelling, require (at least) two-scale numerical approach to finite element (or volume, difference, etc.) computations: i) at the macro-scale for a whole (nearly elastic, partially damaged) body and ii) at the micro-scale near the crack (a new interior surface). The paper presents an always convergent procedure handling overlapping two-scale meshes for such model problems, open to generalizations in many directions.
GLOBALLY SMOOTH SOLUTIONS TO CAUCHY PROBLEM OF A QUASILINEAR HYPERBOLIC SYSTEM ARISING IN BIOLOGY
Institute of Scientific and Technical Information of China (English)
郑永树
2001-01-01
This article considers Cauchy problemut- (uv)x = 0,vt- ux =0, (E)v(x,0) = u0(x) ＞ 0, v(x,0) = v0(x). (Ⅰ)A necessary and sufficient condition in guaranteeing that Cauchy problem admits a global G1-solution on t ＞ 0 is obtained.
Existence and uniqueness of positive solutions to a quasilinear elliptic problem in $R^N$
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Dragos-Patru Covei
2005-12-01
Full Text Available We prove the existence of a unique positive solution to the problem $$ -Delta _{p}u=a(xf(u $$ in $mathbb{R}^{N}$, $N>2$. Our result extended previous works by Cirstea-Radulescu and Dinu, while the proofs are based on two theorems on bounded domains, due to Diaz-Saa and Goncalves-Santos.
Classical solutions of mixed problems for quasilinear first order PFDEs on a cylindrical domain
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Wojciech Czernous
2014-01-01
Full Text Available We abandon the setting of the domain as a Cartesian product of real intervals, customary for first order PFDEs (partial functional differential equations with initial boundary conditions. We give a new set of conditions on the possibly unbounded domain \\(\\Omega\\ with Lipschitz differentiable boundary. Well-posedness is then reliant on a variant of the normal vector condition. There is a neighbourhood of \\(\\partial\\Omega\\ with the property that if a characteristic trajectory has a point therein, then its every earlier point lies there as well. With local assumptions on coefficients and on the free term, we prove existence and Lipschitz dependence on data of classical solutions on \\((0,c\\times\\Omega\\ to the initial boundary value problem, for small \\(c\\. Regularity of solutions matches this domain, and the proof uses the Banach fixed-point theorem. Our general model of functional dependence covers problems with deviating arguments and integro-differential equations.
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Wang Zhigang; Li Yachun
2012-01-01
The aim of this paper is to prove the well-posedness (existence and uniqueness)of the Lp entropy solution to the homogeneous Dirichlet problems for the anisotropic degenerate parabolic-hyperbolic equations with Lp initial value.We use the device of doubling variables and some technical analysis to prove the uniqueness result.Moreover we can prove that the Lp entropy solution can be obtained as the limit of solutions of the corresponding regularized equations of nondegenerate parabolic type.
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Panov, E Yu [Novgorod State University, Novgorod (Russian Federation)
2002-12-31
We construct a theory of locally summable generalized entropy solutions (g.e. solutions) of the Cauchy problem for a first-order non-homogeneous quasilinear equation with continuous flux vector satisfying a linear restriction on its growth. We prove the existence of greatest and least g.e. solutions, suggest sufficient conditions for uniqueness of g.e. solutions, prove several versions of the comparison principle, and obtain estimates for the L{sup p}-norms of solution with respect to the space variables. We establish the uniqueness of g.e. solutions in the case when the input data are periodic functions of the space variables.
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Buerger, R.; Frid, H.; Karlsen, K.H.
2002-07-01
We consider a free boundary problem of a quasilinear strongly degenerate parabolic equation arising from a model of pressure filtration of flocculated suspensions. We provide definitions of generalized solutions of the free boundary problem in the framework of L2 divergence-measure fields. The formulation of boundary conditions is based on a Gauss-Green theorem for divergence-measure fields on bounded domains with Lipschitz deformable boundaries and avoids referring to traces of the solution. This allows to consider generalized solutions from a larger class than BV. Thus it is not necessary to derive the usual uniform estimates on spatial and time derivatives of the solutions of the corresponding regularized problem requires in the BV approach. We first prove existence and uniqueness of the solution of the regularized parabolic free boundary problem and then apply the vanishing viscosity method to prove existence of a generalized solution to the degenerate free boundary problem. (author)
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper, a class of quasi-linear Rie mann-Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H2 to this problem was proved by means of Tikhonov' s fixed point theorem and corresponding theories for general holomorphic functions
A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
YU Xijun
2005-01-01
A combination of the classical Newton Method and the multigrid method, i.e.,a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O(NNk) similar to multigrid method for linear parabolic problems.
Quasilinear evolution equations of the third order
Directory of Open Access Journals (Sweden)
Andrei V. Faminskii
2007-11-01
Full Text Available The present paper is a survey concerned with certain aspects of solvability and well-posedness of initial and initial-boundary value problems for various quasilinear evolution equations of the third order. This class includes, for example, Korteweg-de Vries (KdV and Zakharov-Kuznetsov (ZK equations.
Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces
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Hacer Bozkurt
2014-01-01
Full Text Available Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986. Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005, Talo and Başar (2010, and Nikol'skiĭ (1993. His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.
Institute of Scientific and Technical Information of China (English)
李志伟; 孙宏义
2001-01-01
The layer phenomenon of solution for the Robin problem of quasilinear systemε ″ =F(t,)＋ (t,).a
Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J. B.; Chini, G. P.; Tobias, S. M.
2016-05-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. We present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through nonlocal spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta plane and show that it is accurate even for a small number of large-scale modes. As GQL is formally linear in the small zonal scales, it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems.
The quasilinear parabolic kirchhoff equation
Directory of Open Access Journals (Sweden)
Dawidowski Łukasz
2017-04-01
Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Moving interfaces and quasilinear parabolic evolution equations
Prüss, Jan
2016-01-01
In this monograph, the authors develop a comprehensive approach for the mathematical analysis of a wide array of problems involving moving interfaces. It includes an in-depth study of abstract quasilinear parabolic evolution equations, elliptic and parabolic boundary value problems, transmission problems, one- and two-phase Stokes problems, and the equations of incompressible viscous one- and two-phase fluid flows. The theory of maximal regularity, an essential element, is also fully developed. The authors present a modern approach based on powerful tools in classical analysis, functional analysis, and vector-valued harmonic analysis. The theory is applied to problems in two-phase fluid dynamics and phase transitions, one-phase generalized Newtonian fluids, nematic liquid crystal flows, Maxwell-Stefan diffusion, and a variety of geometric evolution equations. The book also includes a discussion of the underlying physical and thermodynamic principles governing the equations of fluid flows and phase transitions...
On some perturbation techniques for quasi-linear parabolic equations
Directory of Open Access Journals (Sweden)
Igor Malyshev
1990-01-01
Full Text Available We study a nonhomogeneous quasi-linear parabolic equation and introduce a method that allows us to find the solution of a nonlinear boundary value problem in explicit form. This task is accomplished by perturbing the original equation with a source function, which is then found as a solution of some nonlinear operator equation.
Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations
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Umer Saeed
2014-01-01
Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.
Uniqueness of solution of a quasi-linear Reaction-diffusion system
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, we consider nonnegative classical solutions of a Quasi-linear reactiondiffusion system with nonlinear boundary conditions. We prove the uniqueness of a nonnegative classical solution to this problem.
Lyapunov-type inequalities for quasilinear elliptic equations with Robin boundary condition.
Dinlemez Kantar, Ülkü; Özden, Tülay
2017-01-01
The aim of this study is to prove Lyapunov-type inequalities for a quasilinear elliptic equation in [Formula: see text]. Also the lower bound for the first positive eigenvalue of the boundary value problem is obtained.
Institute of Scientific and Technical Information of China (English)
刘存明
2012-01-01
Under the assumptions that the quasilinear hyperbolic system is not weakly linearly degenerate and the boundary functions given on the characteristic boundaries possess small C1 norms and certain decaying properties,by using the characteristic method and the decomposition for waves,we obtain the blow-up mechanism and the asymptotic behavior of the life-span of the C1 solution to the Goursat problem.%对一阶拟线性双曲型方程组的Goursat问题,利用特征线方法及波分解公式,在方程组不是弱线性退化的假设下,当特征边界上给出的边界函数C1范数充分小、且满足一定衰减性时,得到其C1解的破裂机制及关于生命跨度的渐近估计.
Implicit quasilinear differential systems: a geometrical approach
Directory of Open Access Journals (Sweden)
Miguel C. Munoz-Lecanda
1999-04-01
Full Text Available This work is devoted to the study of systems of implicit quasilinear differential equations. In general, no set of initial conditions is admissible for the system. It is shown how to obtain a vector field whose integral curves are the solution of the system, thus reducing the system to one that is ordinary. Using geometrical techniques, we give an algorithmic procedure in order to solve these problems for systems of the form $A(xdot x =alpha (x$ with $A(x$ being a singular matrix. As particular cases, we recover some results of Hamiltonian and Lagrangian Mechanics. In addition, a detailed study of the symmetries of these systems is carried out. This algorithm is applied to several examples arising from technical applications related to control theory.
Quasilinear reformulation of Lovelock gravity
Willison, Steven
2015-01-01
Here we give an extended review of the quasilinear reformulation of the Lovelock gravitational field equations in harmonic gauge presented in 1409.6656 [gr-qc]. This is important in order to establish rigorously well-posedness of the theory perturbed about certain backgrounds. The resulting system is not quasidiagonal, therefore analysis of causality is complicated in general. The conditions for the equations to be Leray hyperbolic are elucidated. The relevance to some recent results regarding the stability analysis of black holes is presented.
Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
Pao, C. V.; Ruan, W. H.
2007-09-01
The aim of this paper is to investigate the existence, uniqueness, and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions, including a system of quasilinear parabolic and ordinary differential equations. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady-state solution. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients Di(ui) may have the property Di(0)=0 for some or all i. Our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations. It is shown that the time-dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a porous medium type of problem, a heat-transfer problem, and a two-component competition model in ecology. These applications illustrate some very interesting distinctive behavior of the time-dependent solutions between density-independent and density-dependent diffusions.
A quasilinear model for solute transport under unsaturated flow
Energy Technology Data Exchange (ETDEWEB)
Houseworth, J.E.; Leem, J.
2009-05-15
We developed an analytical solution for solute transport under steady-state, two-dimensional, unsaturated flow and transport conditions for the investigation of high-level radioactive waste disposal. The two-dimensional, unsaturated flow problem is treated using the quasilinear flow method for a system with homogeneous material properties. Dispersion is modeled as isotropic and is proportional to the effective hydraulic conductivity. This leads to a quasilinear form for the transport problem in terms of a scalar potential that is analogous to the Kirchhoff potential for quasilinear flow. The solutions for both flow and transport scalar potentials take the form of Fourier series. The particular solution given here is for two sources of flow, with one source containing a dissolved solute. The solution method may easily be extended, however, for any combination of flow and solute sources under steady-state conditions. The analytical results for multidimensional solute transport problems, which previously could only be solved numerically, also offer an additional way to benchmark numerical solutions. An analytical solution for two-dimensional, steady-state solute transport under unsaturated flow conditions is presented. A specific case with two sources is solved but may be generalized to any combination of sources. The analytical results complement numerical solutions, which were previously required to solve this class of problems.
A Singular Quasilinear Elliptic Boundary Value Problem%关于一个拟线性椭圆边值问题的研究
Institute of Scientific and Technical Information of China (English)
王俊禹; 郑大伟; 高文杰
2003-01-01
A boundary value problem of a nonlinear partial differential equation with the N-dimensional p-Laplacian as the principal part is studied. The nonlinear term in the equation may have singularity and discontinuity in its variables. A typical form of the equation is the well-known Emden-Fowler equation with negative exponent. The existence and uniqueness results are obtained via a perturbation technique, the Schauder fixed point theorem and careful analysis of the property of the solutions.%本文研究一个主部为N维P-Laplace微分算子的非线性偏微分方程的边值问题.方程中的非线性项关于其变量可以具有奇性和间断性.这类方程的一种典型情形是大家熟知的具负指数的Emden-Fowler方程.本文利用摄动技巧,Schauder不动点定理,经对解的性质的精细分析,获得了解的存在性和唯一性结果.
The Generalized Quasilinear Approximation: Application to Zonal Jets
Marston, J B; Tobias, S M
2016-01-01
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through non-local spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta-plane and show that it is accurate even for a small number of large-scale modes. As this approximation is formally linear in the small zonal scales it allows for the closure of the system...
New Inner Product Quasilinear Spaces on Interval Numbers
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Hacer Bozkurt
2016-01-01
Full Text Available Primarily we examine the new example of quasilinear spaces, namely, “IRn interval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results on IRn interval space related to these concepts. Secondly, we present Is,Ic0,Il∞, and Il2 quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.
Institute of Scientific and Technical Information of China (English)
Xu Yumei
2005-01-01
In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity (＞ 1), a blow-up result is obtained for the C1 solution to the Cauchy problem under the assumptions where there is a simple genuinely nonlinear characteristic and the initial data possess certain weaker decaying properties.
Institute of Scientific and Technical Information of China (English)
王利彬
2003-01-01
In this paper we consider the Cauchy problem for quasilinear hyperbolic systems with characteristics with constant multiplicity. Without restriction on characteristics with constant multiplicity(＞ 1), under the assumptions that there is a genuinely nonlinear simple characteristic and the initial data possess certain decaying properties, the blow-up result is obtained for the C,1 solution to the Cauchy problem.
Difference schemes with intrinsic parallelism for quasi-linear parabolic systems
Institute of Scientific and Technical Information of China (English)
周毓麟
1997-01-01
The boundary value problem for quasi-linear parabolic system is solved by the finite difference method with intrinsic parallelism The existence and uniqueness and convergence theorems of the discrete vector solu tions of the nonlinear difference system with intrinsic parallelism are proved The limiting vector function is just the unique generalized solution of the original problem for the parabolic system
Blow-up Mechanism of Classical Solutions to Quasilinear Hyperbolic Systems in the Critical Case
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.
Quasi-linear symmetric hyperbolic Fuchsian systems in several space dimensions
Ames, Ellery; Isenberg, James; LeFloch, Philippe G
2012-01-01
We establish well-posedness results for the singular initial value problem associated with a class of quasi-linear, symmetric hyperbolic, partial differential equations of Fuchsian type in several space dimensions. This is an extension of earlier work by the authors for the same problem in one space dimension.
Shiryaeva, E V
2014-01-01
In paper [S.I. Senashov, A. Yakhno. 2012. SIGMA. Vol.8. 071] the variant of the hodograph method based on the conservation laws for two hyperbolic quasilinear equations of the first order is described. Using these results we propose a method which allows to reduce the Cauchy problem for the two quasilinear PDE's to the Cauchy problem for ODE's. The proposed method is actually some similar method of characteristics for a system of two hyperbolic quasilinear equations. The method can be used effectively in all cases, when the linear hyperbolic equation in partial derivatives of the second order with variable coefficients, resulting from the application of the hodograph method, has an explicit expression for the Riemann-Green function. One of the method's features is the possibility to construct a multi-valued solutions. In this paper we present examples of method application for solving the classical shallow water equations.
Positive solutions of quasilinear parabolic systems with Dirichlet boundary condition
Pao, C. V.; Ruan, W. H.
Coupled systems for a class of quasilinear parabolic equations and the corresponding elliptic systems, including systems of parabolic and ordinary differential equations are investigated. The aim of this paper is to show the existence, uniqueness, and asymptotic behavior of time-dependent solutions. Also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system. The elliptic operators in both systems are allowed to be degenerate in the sense that the density-dependent diffusion coefficients D(u) may have the property D(0)=0 for some or all i=1,…,N, and the boundary condition is u=0. Using the method of upper and lower solutions, we show that a unique global classical time-dependent solution exists and converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions; and if the maximal and minimal solutions coincide then the steady-state solution is unique and the time-dependent solution converges to the unique solution. Applications of these results are given to three model problems, including a scalar polynomial growth problem, a coupled system of polynomial growth problem, and a two component competition model in ecology.
Directory of Open Access Journals (Sweden)
F. Z. Geng
2012-01-01
Full Text Available We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.
Inference in dynamic systems using B-splines and quasilinearized ODE penalties.
Frasso, Gianluca; Jaeger, Jonathan; Lambert, Philippe
2016-05-01
Nonlinear (systems of) ordinary differential equations (ODEs) are common tools in the analysis of complex one-dimensional dynamic systems. We propose a smoothing approach regularized by a quasilinearized ODE-based penalty. Within the quasilinearized spline-based framework, the estimation reduces to a conditionally linear problem for the optimization of the spline coefficients. Furthermore, standard ODE compliance parameter(s) selection criteria are applicable. We evaluate the performances of the proposed strategy through simulated and real data examples. Simulation studies suggest that the proposed procedure ensures more accurate estimates than standard nonlinear least squares approaches when the state (initial and/or boundary) conditions are not known.
Soliton solutions for a quasilinear Schrodinger equation
Directory of Open Access Journals (Sweden)
Duchao Liu
2013-12-01
Full Text Available In this article, critical point theory is used to show the existence of nontrivial weak solutions to the quasilinear Schrodinger equation $$ -\\Delta_p u-\\frac{p}{2^{p-1}}u\\Delta_p(u^2=f(x,u $$ in a bounded smooth domain $\\Omega\\subset\\mathbb{R}^{N}$ with Dirichlet boundary conditions.
Institute of Scientific and Technical Information of China (English)
Peng QU; Cunming LIU
2012-01-01
For a kind of partially dissipative quasilinear hyperbolic systems without Shizuta-Kawashima condition,in which all the characteristics,except a weakly linearly degenerate one,are involved in the dissipation,the global existence of H2 classical solution to the Cauchy problem with small initial data is obtained.
EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH ZERO EIGENVALUES
Institute of Scientific and Technical Information of China (English)
LI TATSIEN; YU LIXIN
2003-01-01
For a class of mixed initial-boundary value problem for general quasilinear hyperbolic sys-tems with zero eigenvalues, the authors establish the local exact controllability with boundarycontrols acting on one end or on two ends and internal controls acting on a part of equationsin the system.
Asymptotic behavior of solutions to a degenerate quasilinear parabolic equation with a gradient term
Directory of Open Access Journals (Sweden)
Huilai Li
2015-12-01
Full Text Available This article concerns the asymptotic behavior of solutions to the Cauchy problem of a degenerate quasilinear parabolic equations with a gradient term. A blow-up theorem of Fujita type is established and the critical Fujita exponent is formulated by the spacial dimension and the behavior of the coefficient of the gradient term at infinity.
Quasilinear simulations of interplanetary shocks and Earth's bow shock
Afanasiev, Alexandr; Battarbee, Markus; Ganse, Urs; Vainio, Rami; Palmroth, Minna; Pfau-Kempf, Yann; Hoilijoki, Sanni; von Alfthan, Sebastian
2016-04-01
We have developed a new self-consistent Monte Carlo simulation model for particle acceleration in shocks. The model includes a prescribed large-scale magnetic field and plasma density, temperature and velocity profiles and a self-consistently computed incompressible ULF foreshock under the quasilinear approximation. Unlike previous analytical treatments, our model is time dependent and takes full account of the anisotropic particle distributions and scattering in the wave-particle interaction process. We apply the model to the problem of particle acceleration at traveling interplanetary (IP) shocks and Earth's bow shock and compare the results with hybrid-Vlasov simulations and spacecraft observations. A qualitative agreement in terms of spectral shape of the magnetic fluctuations and the polarization of the unstable mode is found between the models and the observations. We will quantify the differences of the models and explore the region of validity of the quasilinear approach in terms of shock parameters. We will also compare the modeled IP shocks and the bow shock, identifying the similarities and differences in the spectrum of accelerated particles and waves in these scenarios. The work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 637324 (HESPERIA). The Academy of Finland is thanked for financial support. We acknowledge the computational resources provided by CSC - IT Centre for Science Ltd., Espoo.
Quasilinear systems with linearizable characteristic webs
Agafonov, S. I.; Ferapontov, E. V.; Novikov, V. S.
2017-07-01
We classify quasilinear systems in Riemann invariants whose characteristic webs are linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic webs on all solutions imposes simple second-order constraints for the characteristic speeds of the system. It is demonstrated that every such system with n >3 components can be transformed by a reciprocal transformation to n uncoupled Hopf equations. All our considerations are local.
Transport phenomena in a plasma quasilinear theory
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Enos D'Ambrogio
1991-05-01
Full Text Available Making use of a recently developed quasi-linear formulation of 1D Vlasov equation, we derive the balance relations for the space-averaged distribution function and spectral power density. The validity-range in the short-time behaviour as well as in the time asymptotic limit is discussed. The formalism is perturbative but non-markovian in character, as it formally generalizes, and in the appropriate limit reproduces, Pocobelli's kinetic theory.
QUASILINEARIZATION, SYSTEM IDENTIFICATION, AND PREDICTION
regime in an effort to improve the quality of the control exerted. A mathematical formulation and computational solution of the problems of system ... identification and the determination of unmeasurable state variables on the basis of observations of a process, two topics of central importance in the
Institute of Scientific and Technical Information of China (English)
ZHOU Yulin; YUAN Guangwei; SHEN Longjun
2004-01-01
A kind of the general finite difference schemes with intrinsicparallelism for the boundary value problem of the quasilinearparabolic system is studied without assuming heuristically thatthe original boundary value problem%for the quasilinear parabolic systemhas the unique smooth vector solution. By the method of a prioriestimation of the discrete solutions of the nonlinear differencesystems, and the interpolation formulas of the various norms ofthe discrete functions and the fixed-pointtechnique in finite dimensional Euclidean space, the existence anduniqueness of the discrete vector solutions of the nonlineardifference system with intrinsic parallelismare proved. Moreover the unconditional stability ofthe general finite difference schemes with intrinsic parallelismis justified in the sense of the continuous dependence of thediscrete vector solution of the difference schemes on the discretedata of the original problems in the discrete W(2,1)2 norms. Finally the convergence of the discrete vector solutions ofthe certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.
Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2 symmetric vacuum spacetimes
Ames, Ellery; Isenberg, James; LeFloch, Philippe G
2012-01-01
We set up the singular initial value problem for quasilinear hyperbolic Fuchsian systems of first order and establish a well-posedness theory for this problem with smooth data and smooth coefficients. We apply this theory in order to show the existence of smooth (although not analytic) T2 symmetric solutions to the vacuum Einstein equations, which exhibit AVTD (asymptotically velocity term dominated) behavior in the neighborhood of their singularities and are polarized or half-polarized.
The Quasilinear Premise for the Modeling of Plasma Turbulence
Howes, Gregory G; TenBarge, Jason M
2014-01-01
The quasilinear premise is a hypothesis for the modeling of plasma turbulence in which the turbulent fluctuations are represented by a superposition of randomly-phased linear wave modes, and energy is transferred among these wave modes via nonlinear interactions. We define specifically what constitutes the quasilinear premise, and present a range of theoretical arguments in support of the relevance of linear wave properties even in a strongly turbulent plasma. We review evidence both in support of and in conflict with the quasilinear premise from numerical simulations and measurements of plasma turbulence in the solar wind. Although the question of the validity of the quasilinear premise remains to be settled, we suggest that the evidence largely supports the value of the quasilinear premise in modeling plasma turbulence and that its usefulness may also be judged by the insights gained from such an approach, with the ultimate goal to develop the capability to predict the evolution of any turbulent plasma syst...
On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
Deruelle, N; Deruelle, Nathalie; Madore, John
2003-01-01
We review some properties of the Einstein-"Gauss-Bonnet" equations for gravity--also called the Einstein-Lanczos equations in five and six dimensions, and the Lovelock equations in higher dimensions. We illustrate, by means of simple Kaluza-Klein and brane cosmological models, some consequences of the quasi-linearity of these equations on the Cauchy problem and structure of characteristics (a point first studied by Yvonne Choquet-Bruhat), as well as on "junction conditions".
Institute of Scientific and Technical Information of China (English)
秦玉明; 李海燕
2014-01-01
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.
Directory of Open Access Journals (Sweden)
Ky Ho
2014-11-01
Full Text Available We establish sufficient conditions for the existence of multiple positive solutions to nonautonomous quasilinear elliptic equations with p(x-Laplacian and sign-changing nonlinearity. For solving the Dirichlet boundary-value problem we use variational and topological methods. The nonexistence of positive solutions is also studied.
Quasi-linear dynamics of Weibel instability
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O. A. Pokhotelov
2011-11-01
Full Text Available The quasi-linear dynamics of resonant Weibel mode is discussed. It is found that nonlinear saturation of Weibel mode is accompanied by substantial modification of the distribution function in resonant region. With the growth of the wave amplitude the parabolic bell-like form of the electron distribution function in this region converts into flatter shape, such as parabola of the fourth order. This results in significant weakening of the resonant interaction of the wave with particles. The latter becomes weaker and then becomes adiabatic interaction with the bulk of the plasma. This is similar to the case of Bernstein-Greene-Kruskal (Bernstein et al., 1957 electrostatic waves. The mathematical similarity of the Weibel and magnetic mirror instabilities is discussed.
The Shear Dynamo: quasilinear kinematic theory
Sridhar, S
2008-01-01
Large--scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is non perturbative in the strength of the background shear. We derive expressions for the turbulent transport coefficients of the mean magnetic field, by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. We prove that, for non helical turbulence, the equation governing the time evolution of the cross shear component of the mean magnetic field is closed, in the sense that it is independent of the other two components. This result is valid for any Galilean--invariant velocity field, independent of its dynamics. Thus we find the shear--current assisted dynamo is essentially absent, although large--scale non helical dynamo action is not ruled out.
Liu, Y.; Li, T.; Zhu, C.; Zhang, R.; Wu, Y.
2015-12-01
Three-dimensional (3-D) electromagnetic (EM) forward modelling and inversion continues to be an important issue for the correct interpretation of EM data.To this end,approximate solutions have been developed that allow the construction of relatively fast forward modelling and inversion schemes.We have developed an improved quasi-linear approximation which is more appropriate in solving the linear equation for greatly shortening calculation time.We achieved this by using green's function properties.Then we introduced the improved quasi-linear approximation to spectral induced polarization (SIP) to tackle the problem of the resolution and the efficiency.The localized quasi-linear (LQL) approximation theory is appropriate for multisource array-type surveys assuming that the normal field is slowly varying within the inhomogeneity domain.However,the normal field of attenuates severely which dose not satisfy the assumption of the LQL approximation.As a consenquence,the imaginary part is not accurate when LQL approximation is adopted for the simulation.The improved quasi-linear approximation provide a new approach with the same resolution of QL approximation and much less calculation time.We have also constructed three-dimensional SIP forward modeling based on improved quasi-linear approximation method.It only takes 0.8s for forward modeling when inhomogeneity domain is divided into 2000 blocks.Beyond that, we have introduced the Cole-Cole model to the algorithm and complete the three-dimensional complex resistivity conjugate gradient inversion with parameter restraint.The model trial results show that this method can obtain good inversion results in physical parameters such as zero frequency resistivity, polarization.The results demonstrate the stability and the efficiency of the improved quasi-linear approximation and the method may be a practical solution for3-D EM forward modelling and inversion of SIP.
EXISTENCE AND UNIQUENESS OF RADIAL SOLUTIONS OF QUASILINEAR EQU ATIONS IN A BALL
Institute of Scientific and Technical Information of China (English)
WeiGongming; ChenZuchi
2002-01-01
We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du)+f(u)=0,u>0,x∈BR(0),u|δBR(0)=0,where A and f are continuous functions in (0,∞) and f is positive in (0,1),f(1)=0. We prove that (1) if f is strictly decreasing,the problem has a unique classical radial solution for any real number R>0;(2)if f is not monotonous,the problem has at least one classical solution for some R>0 large enough.
Controllability of quasilinear stochastic evolution equations in Hilbert spaces
Directory of Open Access Journals (Sweden)
P. Balasubramaniam
2001-01-01
Full Text Available Controllability of the quasilinear stochastic evolution equation is studied using semigroup theory and a stochastic version of the well known fixed point theorem. An application to stochastic partial differential equations is given.
On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order
Institute of Scientific and Technical Information of China (English)
Zhen Hai LIU
2005-01-01
We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order, which can degenerate, on a part of the boundary, on a segment in the interior of the domain and in time.
The homogenization of a class of degenerate quasilinear parabolic equations
Institute of Scientific and Technical Information of China (English)
ZHANG Xingyou; HUANG Yong
2003-01-01
The homogenization of a class of degenerate quasilinear parabolic equations is studied. The Ap weight theory and the classical compensated compactness method are incorporated to obtain the homogenized equation.
Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source
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Pan Zheng
2012-01-01
Full Text Available We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul+uq, (x,t∈RN×(0,T, where N≥1, p>2 , and m, l, q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.
Directory of Open Access Journals (Sweden)
Nicolae Tarfulea
2009-10-01
Full Text Available We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.
Institute of Scientific and Technical Information of China (English)
Yi DU; Zheng An YAO
2011-01-01
In this paper, we consider the Cauchy problem for systems of quasi-linear wave equations with multiple propagation speeds in spatial dimensions n ≥ 4. The problem when the nonlinearities depend on both the unknown function and their derivatives is studied. Based on some Klainerman- Sideris type weighted estimates and space-time L estimates, the results that the almost global existence for space dimensions n = 4 and global existence for n ≥ 5 of small amplitude solutions are presented.
Quasilinear equations with source terms on Carnot groups
Phuc, Nguyen Cong
2012-01-01
In this paper we give necessary and sufficient conditions for the existence of solutions to quasilinear equations of Lane--Emden type with measure data on a Carnot group $\\mathbb G$ of arbitrary step. The quasilinear part involves operators of the $p$-Laplacian type $\\Delta_{\\mathbb G,\\,p}\\,$, $1
quasilinear equations with source terms which has been known only for equations involving the sub-Laplacian ($p=2$) on the Heisenberg group.
A quasi-linear gyrokinetic transport model for tokamak plasmas
Casati, Alessandro
2012-01-01
The development of a quasi-linear gyrokinetic transport model for tokamak plasmas, ultimately designed to provide physically comprehensive predictions of the time evolution of the thermodynamic relevant quantities, is a task that requires tight links among theoretical, experimental and numerical studies. The framework of the model here proposed, which operates a reduction of complexity on the nonlinear self-organizing plasma dynamics, allows in fact multiple validations of the current understanding of the tokamak micro-turbulence. The main outcomes of this work stem from the fundamental steps involved by the formulation of such a reduced transport model, namely: (1) the verification of the quasi-linear plasma response against the nonlinearly computed solution, (2) the improvement of the turbulent saturation model through an accurate validation of the nonlinear codes against the turbulence measurements, (3) the integration of the quasi-linear model within an integrated transport solver.
Parameters Identification for an Abstract Cauchy Problem by Quasilinearization
1989-10-01
if in addition ’ is of bounded variation on (-r,01, then DF(q) satisfies (1111). -12- Proof: Let A = max lakI and IhI = max IhkI Then we obtain the...zero as q 4 q* and (H8) holds. If ’ is of bounded variation on I-r,0, then y and ; are of bounded variation on {-r,TI. By 115, Theorem 2.1.7(b)] this...4.5) satisfies (1110). Moreover, if in addition u is of bounded variation on [0,T], then DG(q) satisfies (H13). Proof: Using (4.5) in place of (4.4
PROGRESSING WAVE SOLUTIONS TO QUASI-LINEAR SYSTEMS MIXED PROBLEMS
Institute of Scientific and Technical Information of China (English)
WANGWEIKE
1994-01-01
The author studies the technique of paradifferential operator defined on a space of conormal distribution with three indeces,and then use this technique to prove that a progressing wave which hits the boundary is reflected according to the usual law.
Parallel difference schemes with interface extrapolation terms for quasi-linear parabolic systems
Institute of Scientific and Technical Information of China (English)
Guang-wei YUAN; Xu-deng HANG; Zhi-qiang SHENG
2007-01-01
In this paper some new parallel difference schemes with interface extrapolation terms for a quasi-linear parabolic system of equations are constructed. Two types of time extrapolations are proposed to give the interface values on the interface of sub-domains or the values adjacent to the interface points, so that the unconditional stable parallel schemes with the second accuracy are formed.Without assuming heuristically that the original boundary value problem has the unique smooth vector solution, the existence and uniqueness of the discrete vector solutions of the parallel difference schemes constructed are proved. Moreover the unconditional stability of the parallel difference schemes is justified in the sense of the continuous dependence of the discrete vector solution of the schemes on the discrete known data of the original problems in the discrete W2(2,1) (Q△) norms. Finally the convergence of the discrete vector solutions of the parallel difference schemes with interface extrapolation terms to the unique generalized solution of the original quasi-linear parabolic problem is proved. Numerical results are presented to show the good performance of the parallel schemes, including the unconditional stability, the second accuracy and the high parallelism.
Institute of Scientific and Technical Information of China (English)
Wenrong DAI
2006-01-01
In this paper, we study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with constant multiple and weakly linearly degenerate characteristic fields. Based on the existence of global classical solution proved by Zhou Yi et al., we show that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions, provided that the total variation and the L1 norm of initial data are sufficiently small.
Fuzzy control of power converters based on quasilinear modelling
Li, C. K.; Lee, W. L.; Chou, Y. W.
1995-03-01
Unlike feedback control by the fuzzy PID method, a new fuzzy control algorithm based on quasilinear modelling of the DC-DC converter is proposed. Investigation is carried out using a buck-boost converter. Simulation results demonstrated that the converter can be regulated with improved performance even when subjected to input disturbance and load variation.
Simulation and quasilinear theory of proton firehose instability
Energy Technology Data Exchange (ETDEWEB)
Seough, Jungjoon [Korean Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama, 930-8555 (Japan); Yoon, Peter H. [University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of); Hwang, Junga [Korean Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Korea, University of Science and Technology, Daejeon (Korea, Republic of)
2015-01-15
The electromagnetic proton firehose instability is driven by excessive parallel temperature anisotropy, T{sub ∥} > T{sub ⊥} (or more precisely, parallel pressure anisotropy, P{sub ∥} > P{sub ⊥}) in high-beta plasmas. Together with kinetic instabilities driven by excessive perpendicular temperature anisotropy, namely, electromagnetic proton cyclotron and mirror instabilities, its role in providing the upper limit for the temperature anisotropy in the solar wind is well-known. A recent Letter [Seough et al., Phys. Rev. Lett. 110, 071103 (2013)] employed quasilinear kinetic theory for these instabilities to explain the observed temperature anisotropy upper bound in the solar wind. However, the validity of quasilinear approach has not been rigorously tested until recently. In a recent paper [Seough et al., Phys. Plasmas 21, 062118 (2014)], a comparative study is carried out for the first time in which quasilinear theory of proton cyclotron instability is tested against results obtained from the particle-in-cell simulation method, and it was demonstrated that the agreement was rather excellent. The present paper addresses the same issue involving the proton firehose instability. Unlike the proton cyclotron instability, however, it is found that the quasilinear approximation enjoys only a limited range of validity, especially for the wave dynamics and for the relatively high-beta regime. Possible causes and mechanisms responsible for the discrepancies are speculated and discussed.
Validating a quasi-linear transport model versus nonlinear simulations
Casati, A.; Bourdelle, C.; Garbet, X.; Imbeaux, F.; Candy, J.; Clairet, F.; Dif-Pradalier, G.; Falchetto, G.; Gerbaud, T.; Grandgirard, V.; Gürcan, Ö. D.; Hennequin, P.; Kinsey, J.; Ottaviani, M.; Sabot, R.; Sarazin, Y.; Vermare, L.; Waltz, R. E.
2009-08-01
In order to gain reliable predictions on turbulent fluxes in tokamak plasmas, physics based transport models are required. Nonlinear gyrokinetic electromagnetic simulations for all species are still too costly in terms of computing time. On the other hand, interestingly, the quasi-linear approximation seems to retain the relevant physics for fairly reproducing both experimental results and nonlinear gyrokinetic simulations. Quasi-linear fluxes are made of two parts: (1) the quasi-linear response of the transported quantities and (2) the saturated fluctuating electrostatic potential. The first one is shown to follow well nonlinear numerical predictions; the second one is based on both nonlinear simulations and turbulence measurements. The resulting quasi-linear fluxes computed by QuaLiKiz (Bourdelle et al 2007 Phys. Plasmas 14 112501) are shown to agree with the nonlinear predictions when varying various dimensionless parameters, such as the temperature gradients, the ion to electron temperature ratio, the dimensionless collisionality, the effective charge and ranging from ion temperature gradient to trapped electron modes turbulence.
Exact boundary controllability of nodal profile for quasilinear hyperbolic systems
Li, Tatsien; Gu, Qilong
2016-01-01
This book provides a comprehensive overview of the exact boundary controllability of nodal profile, a new kind of exact boundary controllability stimulated by some practical applications. This kind of controllability is useful in practice as it does not require any precisely given final state to be attained at a suitable time t=T by means of boundary controls, instead it requires the state to exactly fit any given demand (profile) on one or more nodes after a suitable time t=T by means of boundary controls. In this book we present a general discussion of this kind of controllability for general 1-D first order quasilinear hyperbolic systems and for general 1-D quasilinear wave equations on an interval as well as on a tree-like network using a modular-structure construtive method, suggested in LI Tatsien's monograph "Controllability and Observability for Quasilinear Hyperbolic Systems"(2010), and we establish a complete theory on the local exact boundary controllability of nodal profile for 1-D quasilinear hyp...
Institute of Scientific and Technical Information of China (English)
Longjun Shen; Guangwei Yuan
2003-01-01
In the present work we are going to solve the boundary value problem for the quasilinearparabolic systems of partial differential equations with two space dimensions by the finitedifference method with intrinsic parallelism. Some fundamental behaviors of general finitedifference schemes with intrinsic parallelism for the mentioned problems are studied. By themethod of a priori estimation of the discrete solutions of the nonlinear difference systems,and the interpolation formulas of the various norms of the discrete functions and the fixed-point technique in finite dimensional Euclidean space, the existence of the discrete vectorsolutions of the nonlinear difference system with intrinsic parallelism are proved. Moreoverthe convergence of the discrete vector solutions of these difference schemes to the uniquegeneralized solution of the original quasilinear parabolic problem is proved.
Control of nonlinear systems represented in quasilinear form. Ph.D. Thesis, 1994 Final Report
Coetsee, Josef A.
1993-01-01
Methods to synthesize controllers for nonlinear systems are developed by exploiting the fact that under mild differentiability conditions, systems of the form: x-dot = f(x) + G(x)u can be represented in quasilinear form, viz: x-dot = A(x)x + B(x)u. Two classes of control methods are investigated. The first is zero-look-ahead control, where the control input depends only on the current values of A(x) and B(x). For this case the control input is computed by continuously solving a matrix Riccati equation as the system progresses along a trajectory. The second is controllers with look-ahead, where the control input depends on the future behavior of A(x) and B(x). These controllers use the similarity between quasilinear systems and linear time varying systems to find approximate solutions to optimal control type problems. The methods that are developed are not guaranteed to be globally stable. However in simulation studies they were found to be useful alternatives for synthesizing control laws for a general class of nonlinear systems.
Simulation and quasilinear theory of aperiodic ordinary mode instability
Energy Technology Data Exchange (ETDEWEB)
Seough, Jungjoon [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan); International Research Fellow of the Japan Society for the Promotion of Science, Tokyo (Japan); Yoon, Peter H. [Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of); Hwang, Junga [Korea Astronomy and Space Science Institute, Daejeon (Korea, Republic of); Department of Astronomy and Space Science, University of Science and Technology, Daejeon (Korea, Republic of); Nariyuki, Yasuhiro [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan)
2015-08-15
The purely growing ordinary (O) mode instability driven by excessive parallel temperature anisotropy for high-beta plasmas was first discovered in the 1970s. This instability receives renewed attention because it may be applicable to the solar wind plasma. The electrons in the solar wind feature temperature anisotropies whose upper values are apparently limited by plasma instabilities. The O-mode instability may be important in this regard. Previous studies of O mode instability have been based on linear theory, but the actual solar wind electrons may be in saturated state. The present paper investigates the nonlinear saturation behavior of the O mode instability by means of one-dimensional particle-in-cell simulation and quasilinear theory. It is shown that the quasilinear method accurately reproduces the simulation results.
Generalised quasi-linear approximation of the HMRI
Child, Adam; Marston, Brad; Tobias, Steven
2016-01-01
Motivated by recent advances in Direct Statistical Simulation (DSS) of astrophysical phenomena such as out of equilibrium jets, we perform a Direct Numerical Simulation (DNS) of the helical magnetorotational instability (HMRI) under the generalised quasilinear approximation (GQL). This approximation generalises the quasilinear approximation (QL) to include the self-consistent interaction of large-scale modes, interpolating between fully nonlinear DNS and QL DNS whilst still remaining formally linear in the small scales. In this paper we address whether GQL can more accurately describe low-order statistics of axisymmetric HMRI when compared with QL by performing DNS under various degrees of GQL approximation. We utilise various diagnostics, such as energy spectra in addition to first and second cumulants, for calculations performed for a range of Reynolds and Hartmann numbers (describing rotation and imposed magnetic field strength respectively). We find that GQL performs significantly better than QL in descri...
On a class of quasilinear Schr(o)dinger equations
Institute of Scientific and Technical Information of China (English)
SHU Ji; ZHANG Jian
2007-01-01
A type of quasilinear Schr(o)dinger equations in two space dimensions which describe attractive Bose-Einstein condensates in physics is discussed. By establishing the property of the equation and applying the energy method, the blowup of solutions to the equation are proved under certain conditions. At the same time, by the variational method, a sufficient condition of global existence which is related to the ground state of a classical elliptic equation is obtained.
Existence of solutions to quasilinear Schrodinger equations with indefinite potential
Directory of Open Access Journals (Sweden)
Zupei Shen
2015-04-01
Full Text Available In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(xu-(|u| ^2''u=f(u $$ on $\\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.
Existence of multiple solutions for quasilinear diagonal elliptic systems
Directory of Open Access Journals (Sweden)
Marco Squassina
1999-05-01
Full Text Available Nonsmooth-critical-point theory is applied in proving multiplicity results for the quasilinear symmetric elliptic system $$ -sum_{i,j=1}^{n}D_j(a^{k}_{ij}(x,uD_iu_k+ {1over 2}sum_{i,j=1}^{n}sum_{h=1}^N D_{s_k}a^{h}_{ij}(x,uD_iu_hD_ju_h=g_k(x,u,, $$ for $k=1,..,N$.
Quasilinear Carbon Transport In An Impurity Hole Plasma In LHD
Energy Technology Data Exchange (ETDEWEB)
Mikkelsen, David R. [PPPL; Tanaka, K. [NIFS; Nunami, M. [NIFS; Watanabe, T-H. [Nagoya University; Sugama, H. [NIFS; Yoshinuma, M. [NIFS; Suzuki, Y. [NIFS; Goto, M. [NIFS; Morita, S. [NIFS; Wieland, B. [NIFS; Yamada, I. [NIFS; Yashura, R. [NIFS; Akiyama, T. [NIFS; Pablant, Novimir A. [PPPL
2014-04-01
Comprehensive electrostatic gyrokinetic linear stability calculations for ion-scale microinstabilities in an LHD plasma with an ion-ITB and carbon "impurity hole" are used to make quasilinear estimates of particle flux to explore whether microturbulence can explain the observed outward carbon fluxes that flow "up" the impurity density gradient. The ion temperature is not stationary in the ion-ITB phase of the simulated discharge, during which the core carbon density decreases continuously. To fully sample these varying conditions the calculations are carried out at three radial locations and four times. The plasma parameter inputs are based on experimentally measured profiles of electron and ion temperature, as well as electron and carbon density. The spectroscopic line-average ratio of hydrogen and helium densities is used to set the density of these species. Three ion species (H,He,C) and the electrons are treated kinetically, including collisions. Electron instability drive does enhance the growth rate significantly, but the most unstable modes have characteristics of ion temperature gradient (ITG) modes in all cases. As the carbon density gradient is scanned between the measured value and zero, the quasilinear carbon flux is invariably inward when the carbon density profile is hollow, so turbulent transport due to the instabilities considered here does not explain the observed outward flux of impurities in impurity hole plasmas. The stiffness of the quasilinear ion heat flux is found to be 1.7-2.3, which is lower than several estimates in tokamaks.
Positive radially symmetric solution for a system of quasilinear biharmonic equations in the plane
Directory of Open Access Journals (Sweden)
Joshua Barrow
2015-01-01
Full Text Available We study the boundary value system for the two-dimensional quasilinear biharmonic equations $$\\displaylines{ \\Delta (|\\Delta u_i|^{p-2}\\Delta u_i=\\lambda_iw_i(xf_i(u_1,\\ldots,u_m,\\quad x\\in B_1,\\cr u_i=\\Delta u_i=0,\\quad x\\in\\partial B_1,\\quad i=1,\\ldots,m, }$$ where $B_1=\\{x\\in\\mathbb{R}^2:|x|<1\\}$. Under some suitable conditions on $w_i$ and $f_i$, we discuss the existence, uniqueness, and dependence of positive radially symmetric solutions on the parameters $\\lambda_1,\\ldots,\\lambda_m$. Moreover, two sequences are constructed so that they converge uniformly to the unique solution of the problem. An application to a special problem is also presented.
The Existence of Positive Bounded Entire Solutions of Second Order Quasilinear Elliptic Equations
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
In this paper we are concerned with the existence of positive entire solutions of second order quasilinear elliptic equations of the type div(|Du|p-2Du)+f(x,u)=0, x∈RN, (1) where f(x, u) is a continuous function on RN×(0,∞). This problem appears in the study of non-Newtonian fluids and non-Newtonian filtration. The quantity p is a characteristic of the madium. Media with p>2 are called dilatant fluids and those with p<2 are called pseudoplastics. If p=2, they are Newtonian fluid. In the present paper we give new sufficient conditions which ensure the existence of positive entire solutions of (1).When p=2, the related results have been obtained by [1,2]. Our theorem for existence complement and extent to the results by [1,2].
Beyer, Horst Reinhard
2007-01-01
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups. The theoretical part is accessible to graduate students with basic knowledge in functional analysis. Only some examples require more specialized knowledge from the spectral theory of linear, self-adjoint operators in Hilbert spaces. Particular stress is on equations of the hyperbolic type since considerably less often treated in the literature. Also, evolution equations from fundamental physics need to be compatible with the theory of special relativity and therefore are of hyperbolic type. Throughout, detailed applications are given to hyperbolic partial differential equations occurring in problems of current theoretical physics, in particular to Hermitian hyperbolic systems. This volume is thus also of interest to readers from theoretical physics.
Particle Dynamics under Quasi-linear Interaction with Electromagnetic Waves
Energy Technology Data Exchange (ETDEWEB)
Castejon, F.; Eguilior, S.
2003-07-01
Langevin equations for quasi-linear wave particle interaction are obtained taking advantage of the unique vocal equivalence between Fokker-Plank equation and the former ones. Langevin equations are solved numerically and, hence, the evolution of a single particle embedded in an electromagnetic field in momentum space is obtained. The equations are relativistic and valid for any wave. It is also shown that the stochastic part of the equations is negligible in comparison with the deterministic term, except for the momentum to the resonance condition for the main parallel refractive index. (Author) 24 refs.
Preliminary group classification of quasilinear third-order evolution equations
Institute of Scientific and Technical Information of China (English)
Ding-jiang HUANG; Hong-qing ZHANG
2009-01-01
Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transfor-mations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non-equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.
Existence of infinitely many radial solutions for quasilinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Gui Bao
2014-10-01
Full Text Available In this article we prove the existence of radial solutions with arbitrarily many sign changes for quasilinear Schrodinger equation $$ -\\sum_{i,j=1}^{N}\\partial_j(a_{ij}(u\\partial_iu +\\frac{1}{2}\\sum_{i,j=1}^{N}a'_{ij}(u\\partial_iu\\partial_ju+V(xu =|u|^{p-1}u,~x\\in\\mathbb{R}^N, $$ where $N\\geq3$, $p\\in(1,\\frac{3N+2}{N-2}$. The proof is accomplished by using minimization under a constraint.
Keller-Osserman estimates for some quasilinear elliptic systems
Bidaut-Véron, Marie-Françoise; Yarur, Cecilia
2011-01-01
In this article we study quasilinear multipower systems of two equations of two types, in a domain \\Omega of R^{N} : with absorption terms, or mixed terms. Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type. Concerning the mixed system, we show that one of the solutions always satisfies Harnack inequality. In the case \\Omega=B(0,1)\\{0}, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results.
Quasi-Linear Algebras and Integrability (the Heisenberg Picture
Directory of Open Access Journals (Sweden)
Alexei Zhedanov
2008-02-01
Full Text Available We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution interpretation of the corresponding integrable systems.
ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLIC WAVES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping utt+ut-div(a(△u)△u)=01and show that, at least when n≤3, they tend, as t→+∞, to those of the nonlinear parabolic equation ut-div(a(△u)△u)=01in the sense that the norm ‖u(.,t)-v(.,t)‖L∞(Rn)of the difference u-v decays faster than that of either u or v. This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves, first observed by Hsiao, L. and Liu Taiping (see [1,2]).
ON THE NUMERICAL SOLUTION OF QUASILINEAR WAVE EQUATION WITH STRONG DISSIPATIVE TERM
Institute of Scientific and Technical Information of China (English)
Aytekin Gülle
2004-01-01
The numerical solution for a type of quasilinear wave equation is studied. The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved. The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.
Exact Boundary Controllability for a Kind of Second-Order Quasilinear Hyperbolic Systems
Institute of Scientific and Technical Information of China (English)
Ke WANG
2011-01-01
Based on the theory of semi-global C1 solution and the local exact boundary controllability for first-order quasilinear hyperbolic systems,the local exact boundary controllability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.
A quasi-linear parabolic system of chemotaxis
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n -dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A ( u , and that the diffusion coefficient of v is a positive constant. If A ( u is a positive constant, the system is referred to as so-called Keller-Segel system. In the case where the domain is a bounded domain of two-dimensional Euclidean space, it is shown that some solutions to Keller-Segel system blow up in finite time. In three and more dimensional cases, it is shown that solutions to so-called Nagai system blow up in finite time. Nagai system is introduced by Nagai. The diffusion coefficients of Nagai system are positive constants. In this paper, we describe that solutions to the quasi-linear parabolic system exist globally in time, if the positive function A ( u rapidly increases with respect to u .
Quasilinear saturation of the aperiodic ordinary mode streaming instability
Energy Technology Data Exchange (ETDEWEB)
Stockem Novo, A., E-mail: anne@tp4.rub.de; Schlickeiser, R. [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum-und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Yoon, P. H. [Institute for Physical Science & Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin-Si, Gyeonggi-Do 446-701 (Korea, Republic of); Lazar, M. [Institut für Theoretische Physik, Lehrstuhl IV: Weltraum-und Astrophysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Poedts, S. [Centre for Mathematical Plasma Astrophysics, Celestijnenlaan 200B, 3001 Leuven (Belgium); Seough, J. [Faculty of Human Development, University of Toyama, 3190, Gofuku, Toyama City, Toyama 930-8555 (Japan); International Research Fellow of the Japan Society for the Promotion of Science, Tokyo (Japan)
2015-09-15
In collisionless plasmas, only kinetic instabilities and fluctuations are effective in reducing the free energy and scatter plasma particles, preventing an increase of their anisotropy. Solar energetic outflows into the interplanetary plasma give rise to important thermal anisotropies and counterstreaming motions of plasma shells, and the resulting instabilities are expected to regulate the expansion of the solar wind. The present paper combines quasilinear theory and kinetic particle-in-cell simulations in order to study the weakly nonlinear saturation of the ordinary mode in hot counter-streaming plasmas with a temperature anisotropy as a follow-up of the paper by Seough et al. [Phys. Plasmas 22, 082122 (2015)]. This instability provides a plausible mechanism for the origin of dominating, two-dimensional spectrum of transverse magnetic fluctuations observed in the solar wind. Stimulated by the differential motion of electron counterstreams the O mode instability may convert their free large-scale energy by nonlinear collisionless dissipation on plasma particles.
Existence results for quasilinear elliptic systems in RN
Directory of Open Access Journals (Sweden)
N. M. Stavrakakis
1999-10-01
Full Text Available We prove existence results for the quasilinear elliptic system $$ displaylines{ -Delta_{p}u = lambda a(x|u|^{gamma-2}u +lambda b(x |u|^{alpha -1}|v|^{Beta +1}u, cr -Delta_{q}v = lambda d(x|v|^{delta-2}v +lambda b(x|u|^{alpha +1}|v|^{Beta -1}v,, cr }$$ where $gamma$ and $delta$ may reach the critical Sobolev exponents, and the coefficient functions $a$, $b$, and $d$ may change sign. For the unperturbed system ($a=0$, $b=0$, we establish the existence and simplicity of a positive principal eigenvalue, under the assumption that $u(x>0$, $v(x>0$, and $lim_{|x| o infty} u(x =lim_{|x| o infty} u(x=0$.
On linear degeneracy of integrable quasilinear systems in higher dimensions
Ferapontov, E V; Klein, C
2010-01-01
We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be linearly degenerate. We prove this conjecture in the 2-component case, providing a complete classification of multi-dimensional integrable systems in question. In particular, our results imply the non-existence of 2-component integrable systems of hydrodynamic type for $d\\geq 6$. In the second half of the paper we discuss a numerical and analytical evidence for the impossibility of the breakdown of smooth initial data for linearly degenerate systems in 2+1 dimensions.
Validity of quasilinear theory: refutations and new numerical confirmation
Energy Technology Data Exchange (ETDEWEB)
Besse, Nicolas; Bertrand, Pierre [UMR 7198 CNRS-Nancy Universites, Universite Henri Poincare, Bd des Aiguillettes, BP 70239, FR-54506 Vandoeuvre-les-Nancy Cedex (France); Elskens, Yves; Escande, D F, E-mail: nicolas.besse@iecn.u-nancy.fr, E-mail: yves.elskens@univ-provence.fr, E-mail: dominique.escande@univ-provence.fr [UMR 6633 CNRS-Universite de Provence, Faculte de St Jerome, Case 321, Av. Normandie Niemen, FR-13397 Marseille Cedex 20 (France)
2011-02-15
The validity of quasilinear (QL) theory describing the weak warm beam-plasma instability has been a controversial topic for several decades. This issue is tackled anew, both analytically and by numerical simulations which benefit from the power of modern computers and from the development in the last decade of Vlasov codes endowed with both accuracy and weak numerical diffusion. Self-consistent numerical simulations within the Vlasov-wave description show that QL theory remains valid in the strong chaotic diffusion regime. However, there is a non-QL regime before saturation, which confirms previous analytical work and numerical simulation, but contradicts another analytical work. We show analytically the absence of mode coupling in the saturation regime of the instability where a plateau is present in the tail of the particle distribution function. This invalidates several analytical works trying to prove or to contradict the validity of QL theory in the strongly nonlinear regime of the weak warm beam-plasma instability.
NONRADIAL POSITIVE SOLUTIONS TO SINGULAR QUASILINEAR ELLIPTIC EQUATIONS IN THE PLANE
Institute of Scientific and Technical Information of China (English)
Jiongqi Wu
2009-01-01
This paper investigates 2-dimensional singular, quasilinear elliptic equations and gives some sufficient conditions ensuring the equations have infinitely many positive entire solutions. The super-subsolution method is used to prove the existence of such solutions.
Yang, Zhijian; Liu, Zhiming
2017-03-01
The paper investigates the well-posedness and the longtime dynamics of the quasilinear wave equations with structural damping and supercritical nonlinearities: {{u}tt}- Δ u+{{≤ft(- Δ \\right)}α}{{u}t}-\
Institute of Scientific and Technical Information of China (English)
Ling DING; Chunlei TANG
2013-01-01
The existence and multiplicity of positive solutions are studied for a class of quasilinear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
A Class of Quasilinear Parabolic Systems with Cross—Diffusion Effects
Institute of Scientific and Technical Information of China (English)
WanliYANG
1999-01-01
This paper,using the duality technique and Hoelder's inequality,proves the global existence of solutions for a class of the quasilinear parabolic systems with Crossdiffusion effects and competition interaction on and smooth bounded domain in RN.
Wang, Junping
2011-01-01
This paper derives some maximum principles for P1-conforming finite element approximations of quasi-linear second order elliptic equations. The results are extensions of the classical maximum principles in the theory of partial differential equations to finite element methods. The mathematical tools are also extensions of the variational approach that was used in classical PDE theories. The maximum principles for finite element approximations are valid with some geometric conditions that are applied to the angles of each element. For the general quasi-linear elliptic equation, each triangle or tetrahedron needs to be $O(h^\\alpha)$-acute in the sense that each angle $\\alpha_{ij}$ (for triangle) or interior dihedral angle $\\alpha_{ij}$ (for tetrahedron) must satisfy $\\alpha_{ij}\\le \\pi/2-\\gamma h^\\alpha$ for some $\\alpha\\ge 0$ and $\\gamma>0$. For the Poisson problem where the differential operator is given by Laplacian, the angle requirement is the same as the classical one: either all the triangles are non-obt...
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-05-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
Integrable Magnetic Geodesic Flows on 2-Torus: New Examples via Quasi-Linear System of PDEs
Agapov, S. V.; Bialy, M.; Mironov, A. E.
2017-01-01
For a magnetic geodesic flow on the 2-torus the only known integrable example is that of a flow integrable for all energy levels. It has an integral linear in momenta and corresponds to a one parameter group preserving the Lagrangian function of the magnetic flow. In this paper the problem of integrability on a single energy level is considered. Then, in addition to the example mentioned above, a few other explicit examples with quadratic in momenta integrals can be constructed by means of the Maupertuis' principle. Recently we proved that such an integrability problem can be reduced to a remarkable semi-Hamiltonian system of quasi-linear PDEs and to the question of the existence of smooth periodic solutions for this system. Our main result of the present paper states that any Liouville metric with the zero magnetic field on the 2-torus can be analytically deformed to a Riemannian metric with a small magnetic field so that the magnetic geodesic flow on an energy level is integrable by means of an integral quadratic in momenta.
On the Cauchy Problem Describing an Electron-Phonon Interaction
Institute of Scientific and Technical Information of China (English)
Jo(a)o-Paulo DIAS; Mário FIGUEIRA; Filipe OLIVEIRA
2011-01-01
In this paper, a model is derived to describe a quartic anharmonic interatomic interaction with an external potential involving a pair electron-phonon. The authors study the corresponding Cauchy Problem in the semilinear and quasilinear cases.
Kinetic theory and quasilinear theories of jet dynamics
Bouchet, F; Tangarife, T
2016-01-01
We review progress that has been made to constructa theory for the jet formation and maintenance in planetary atmospheres. The theory is built in the regime where velocityfluctuations around the base jet are very small compared to the zonaljet velocity itself. Such situations are frequent in many naturaljets, for instance in the atmosphere of outer planets, the most prominentexample being probably Jupiter's troposphere jets. As discussed inother chapters of this book, fluctuations close to Jupiter zonaljets are smaller than the zonal jets themselves. In such a regime, it is natural and often justified to treat the non-zonalpart of the dynamics with a quasi-linear approximation: at leadingorder the dynamics of the non-zonal flow is described by theequation linearized close to the quasi-stationary zonal jets. The theory, based on a multi-scale method called stochastic averaging, share similarities with Stochastic Structural Stability Theory (S3T) and with second order closure(CE2), also discussed in other chapt...
1981-09-01
norma : Ilfl sup If(tx)I (t,x) e R(S) If(t 1,x)-f(t 2,x)I Q If(t,xI)-f(t,x2) I H t] - sup , H (U - cup , (4.6) (t.,x),(t ,x) It -t2 I (t,x 1),t,x2 ) iXl...introducing appropriate variables, the method of iteration, a priori estimation and fixed point theorems. ISI
Energy Technology Data Exchange (ETDEWEB)
Misguich, J.H
2004-04-01
As a first step toward a nonlinear renormalized description of turbulence phenomena in magnetized plasmas, the lowest order quasi-linear description is presented here from a unified point of view for collisionless as well as for collisional plasmas in a constant magnetic field. The quasi-linear approximation is applied to a general kinetic equation obtained previously from the Klimontovich exact equation, by means of a generalised Dupree-Weinstock method. The so-obtained quasi-linear description of electromagnetic turbulence in a magnetoplasma is applied to three separate physical cases: -) weak electrostatic turbulence, -) purely magnetic field fluctuations (the classical quasi-linear results are obtained for cosmic ray diffusion in the 'slab model' of magnetostatic turbulence in the solar wind), and -) collisional kinetic equations of magnetized plasmas. This mathematical technique has allowed us to derive basic kinetic equations for turbulent plasmas and collisional plasmas, respectively in the quasi-linear and Landau approximation. In presence of a magnetic field we have shown that the systematic use of rotation matrices describing the helical particle motion allows for a much more compact derivation than usually performed. Moreover, from the formal analogy between turbulent and collisional plasmas, the results derived here in detail for the turbulent plasmas, can be immediately translated to obtain explicit results for the Landau kinetic equation.
Orbit-averaged quasilinear diffusion operator in the ion-cyclotron range of frequencies
Energy Technology Data Exchange (ETDEWEB)
Belmondo, V; Bilato, R; Brambilla, M; Maj, O, E-mail: vtb@ipp.mpg.de
2010-11-01
The absorption of radio-frequency waves in the ion-cyclotron range of frequencies (ICRF) in fusion plasmas is adequately described in the frame of the quasilinear theory. A peculiarity of ICRF heating is to increase the fraction of trapped particles, whose the guiding-center trajectories are typically banana orbits with finite width. One possible way to properly account for the effects due to the finite-width orbits is provided by the orbit-averaged quasilinear theory. Here, we propose a routine for the evaluation of the orbit-averaged quasilinear diffusion tensor, given the the wave fields from the full wave code TORIC. Particular care is taken in the evaluation of the contribution of each wave-particle resonance as well as for the transition between the two regimes of correlated and uncorrelated resonances along the orbit. We discuss the quasilinear diffusion coefficient thus obtained and validate the result by comparing the power deposition profile computed from the orbit-averaged quasilinear operator with the one determined by TORIC. For future applications, a novel algorithm for the calculation of the corresponding Monte Carlo operators is also presented.
Vladimirov, Igor G
2012-01-01
The paper is concerned with open quantum systems whose Heisenberg dynamics are described by quantum stochastic differential equations driven by external boson fields. The system-field coupling operators are assumed to be quadratic polynomials of the system observables, with the latter satisfying canonical commutation relations. In combination with a cubic system Hamiltonian, this leads to a class of quasilinear quantum stochastic systems which retain algebraic closedness in the evolution of mixed moments of the observables. Although such a system is nonlinear and its quantum state is no longer Gaussian, the dynamics of the moments of any order are amenable to exact analysis, including the computation of their steady-state values. In particular, a generalized criterion is developed for quadratic stability of the quasilinear systems. The results of the paper are applicable to the generation of non-Gaussian quantum states with manageable moments and an optimal design of linear quantum controllers for quasilinear...
Is the Regge Trajectory Quasi-linear or Square-root Form?
Li, Zhen
2016-01-01
There are many orbital excited mesons discovered in recent years. In this work we attempt to study whether the Regge trajectory is quasi-linear or square-root form. In the framework of the quasi-linear Regge trajectory and square-root Regge trajectory, the masses of the states lying on the well established 11S0, 13S1, and 13P2 trajectories are estimated. Comparison of the results given by the two trajectories with the existing experimental data illustrates that both of them can give a reasonable description for the ground mesons. For the orbital excited states, the quasi-linear trajectory describes the existing meson spectrum to be more reasonable.
Idealized Quasi-Linear Convective Storms Crossing Over Coastlines
Lombardo, K.
2015-12-01
As organized coastal convective storms develop over land and move over a coastal ocean, their storm-scale structures, intensity, and associated weather threats evolve. This study aims to identify and quantify the fundamental mechanisms controlling the evolution of coastal quasi-linear convective systems (QLCSs) as they move offshore, as well as characterize the environmental conditions that support a phase space of life cycles. Results from this work will contribute to the improved predictability of these potentially severe warm season storms. The current work uses the Cloud Model 1 (CM1; Bryan and Fritsch 2002) to systematically study the interaction between QLCSs and marine atmospheric boundary layers (MABLs) associated with the coastal ocean in an idealized numerical framework. The initial simulations are run in 2-dimensions, with a 250 m horizontal resolution and a vertical resolution ranging from 100 m in the lowest 3000 m stretched to 250 m at the top of the 20 km domain. All simulations use the Weisman-Klemp analytic sounding as the base-state sounding profile in conjunction with an RKW-type wind profile. To create a numerical environment representative of a coastal region, the western half of the 800 km domain is configured to represent a land surface, while the eastern half represents a water surface. A series of sensitivity experiments are conducted to explore the influence of sea surface temperature and the associated marine atmospheric boundary layer on coastal QLCSs. Sea surface temperature values are selected to represent values observed within the Mid-Atlantic Bight coastal waters during the warm season, ranging from 14oC ('early summer') to 23oC ('late summer'). The numerical MABL is allowed to develop in time through surface heat fluxes. This presentation will discuss preliminary results from the 'early summer' and 'late summer' SST sensitivity experiments. Preliminary simulations indicate that the 'early summer' QLCS moves more quickly than the
Local classification of stable geometric solutions of systems of quasilinear first-order PDE
Institute of Scientific and Technical Information of China (English)
LI; Bing(李兵); LI; Yangcheng(李养成)
2002-01-01
Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.
The Optimal Control of Second Order Quasi-Linear Equipotential Flows
Directory of Open Access Journals (Sweden)
Victor Onomza WAZIRI
2007-01-01
Full Text Available This research studies the optimal control of Laplacian group of equations of the second differential order and quasilinear or first degree equations in nature. The study categorizes the research into one- through to the nth-dimensional cases as points of generalization. The numerical values and physical Simulates give visual conceptions of the one-to three-dimensional equipotential flows.
SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE
Institute of Scientific and Technical Information of China (English)
Xiao-wu Lu
2001-01-01
A class of finite difference methods of first- and second-order accuracy for the computa tion of solutions to the quasilinear wave equations is presented. These difference methods are constructed based on the symplectic schemes to the infinite-dimensional Hamiltonian system. Numerical experiments are presented to demonstrate the superior performance of these methods.
Soliton solutions for a quasilinear Schrödinger equation via Morse theory
Indian Academy of Sciences (India)
Duchao Liu; Peihao Zhao
2015-08-01
In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrödinger equation of the form $$- u - \\frac{p}{2^{p-1}} u _p (u^2) = f(x, u)$$ in a bounded smooth domain $ \\subset \\mathbb{R}^N$ with Dirichlet boundary condition.
Directory of Open Access Journals (Sweden)
Krishnan Balachandran
2011-06-01
Full Text Available We establish sufficient conditions for controllability of neutral impulsive stochastic quasilinear integrodifferential systems with nonlocal conditions in Hilbert spaces. The results are obtained by using semigroup theory, evolution operator and a fixed point technique. An example is provided to illustrate the obtained results.
Directory of Open Access Journals (Sweden)
Tengfei Shen
2015-12-01
Full Text Available This paper deals with the multiplicity of solutions for Dirichlet boundary conditions of second-order quasilinear equations with impulsive effects. By using critical point theory, a new result is obtained. An example is given to illustrate the main result.
Sarfraz, M.; Yoon, P. H.; Saeed, Sundas; Abbas, G.; Shah, H. A.
2017-01-01
A number of different microinstabilities are known to be responsible for regulating the upper bound of temperature anisotropies in solar wind protons, alpha particles, and electrons. In the present paper, quasilinear kinetic theory is employed to investigate the time variation in electron temperature anisotropies in response to the excitation of parallel electron firehose instability in homogeneous and non-collisional solar wind plasma under the condition of T∥e>T⊥e . By assuming the bi-Maxwellian form of velocity distribution functions, various velocity moments of the particle kinetic equation are taken in order to reduce the theory to macroscopic model in which the wave-particle interaction is incorporated, hence, the macroscopic quasilinear theory. The threshold condition for the parallel electron firehose instability, empirically constructed as a curve in (β∥e,T⊥e/T∥e) phase space, is implicit in the present macroscopic quasilinear calculation. Even though the present calculation excludes the oblique firehose instability, which is known to possess a higher growth rate, the basic methodology may be further extended to include such a mode. Among the findings is that the parallel electron firehose instability dynamically couples the electrons and protons, which implies that this instability may be important for overall solar wind dynamics. The present analysis shows that the macroscopic quasilinear approach may eventually be incorporated in global-kinetic models of the solar wind electrons and ions.
ON THE EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS
Institute of Scientific and Technical Information of China (English)
杨作东; 陆启韶
2001-01-01
We study the existence of positive radial solutions for a class of quasilinear elliptic systems in a ball domains via the blowing up argument and degree theory.The main results of the present paper are new and extend the previously known results.
Solutions to quasi-linear differential equations with iterated deviating arguments
Directory of Open Access Journals (Sweden)
Rajib Haloi
2014-12-01
Full Text Available We establish sufficient conditions for the existence and uniqueness of solutions to quasi-linear differential equations with iterated deviating arguments, complex Banach space. The results are obtained by using the semigroup theory for parabolic equations and fixed point theorems. The main results are illustrated by an example.
The blowup mechanism for 3-D quasilinear wave equations with small data
Institute of Scientific and Technical Information of China (English)
尹会成
2000-01-01
For a class of special three-dimensional quasilinear wave equations, we study the blowup mechanism of classical solutions. More precisely, under the nondegenerate conditions, any radially symmetric solution with small initial data is shown to develop singularities in the second order derivatives while the first order derivatives and itself remain continuous, moreover the blowup of solution is of "cusp type".
Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian
Jiri Benedikt; Vladimir E. Bobkov; Petr Girg; Lukas Kotrla; Peter Takac
2015-01-01
We construct a positive solution to a quasilinear parabolic problem in a bounded spatial domain with the p-Laplacian and a nonsmooth reaction function. We obtain nonuniqueness for zero initial data. Our method is based on sub- and supersolutions and the weak comparison principle. Using the method of sub- and supersolutions we construct a positive solution to a quasilinear parabolic problem with the p-Laplacian and a reaction function that is non-Lipschitz on a ...
Numerical methods for hyperbolic differential functional problems
Directory of Open Access Journals (Sweden)
Roman Ciarski
2008-01-01
Full Text Available The paper deals with the initial boundary value problem for quasilinear first order partial differential functional systems. A general class of difference methods for the problem is constructed. Theorems on the error estimate of approximate solutions for difference functional systems are presented. The convergence results are proved by means of consistency and stability arguments. A numerical example is given.
The quasilinear theory in the approach of long-range systems to quasi-stationary states
Campa, Alessandro; Chavanis, Pierre-Henri
2017-05-01
We develop a quasilinear theory of the Vlasov equation in order to describe the approach of systems with long-range interactions to quasi-stationary states. The quasilinear theory is based on the assumption that, although the initial distribution is not Vlasov stable, nevertheless its evolution towards a Vlasov stable stationary state is such that it is always only slightly inhomogeneous. We derive a diffusion equation governing the evolution of the velocity distribution of the system towards a steady state. This steady state is expected to correspond to the space-averaged quasi-stationary distribution function reached by the Vlasov equation as a result of a collisionless relaxation. We compare the prediction of the quasilinear theory to direct numerical simulations of the Hamiltonian mean field model, starting from an unstable spatially homogeneous distribution, either Gaussian or semi-elliptical. In the Gaussian case, we find that the quasilinear theory works reasonably well for weakly unstable initial conditions (i.e. close to the critical energy ε_c=3/4=0.75 ) and that it is able to predict the energy ε_t≃ 0.735 marking the effective out-of-equilibrium phase transition between unmagnetized and magnetized quasi-stationary states found in the numerical simulations. Similarly, the quasilinear theory works well for energies close to the instability threshold of the semi-elliptical case ε^*c =5/8=0.625 , and it predicts an effective out-of-equilibrium transition at εt≃ 0.619 . In both situations, the quasilinear theory works less well at energies lower than the out-of-equilibrium transition, the disagreement with the numerical simulations increasing with decreasing energy. In that case, we observe, in agreement with our previous numerical study (Campa and Chavanis 2013 Eur. Phys. J. B 86 170), that the quasi-stationary states are remarkably well fitted by polytropic distributions (Tsallis distributions) with index n = 2 (Gaussian case) or n
Shiryaeva, E V
2015-01-01
The paper presents the solutions for the zonal electrophoresis equations are obtained by analytical and numerical methods. The method proposed by the authors is used. This method allows to reduce the Cauchy problem for two hyperbolic quasilinear PDE's to the Cauchy problem for ODE's. In some respect, this method is analogous to the method of characteristics for two hyperbolic equations. The method is effectively applicable in all cases when the explicit expression for the Riemann-Green function of some linear second order PDE, resulting from the use of the hodograph method for the original equations, is known. One of the method advantages is the possibility of constructing a multi-valued solutions. Compared with the previous authors paper, in which, in particular, the shallow water equations are studied, here we investigate the case when the Riemann-Green function can be represent as the sum of the terms each of them is a product of two multipliers depended on different variables. The numerical results for zo...
Multispecies Density and Temperature Gradient Dependence of Quasilinear Particle and Energy Fluxes
Energy Technology Data Exchange (ETDEWEB)
G. Rewoldt; R.V. Budny; W.M. Tang
2004-08-09
The variations of the normalized quasilinear particle and energy fluxes with artificial changes in the density and temperature gradients, as well as the variations of the linear growth rates and real frequencies, for ion temperature gradient and trapped-electron modes, are calculated. The quasilinear fluxes are normalized to the total energy flux, summed over all species. Here, realistic cases for tokamaks and spherical torii are considered which have two impurity species. For situations where there are substantial changes in the normalized fluxes, the ''diffusive approximation,'' in which the normalized fluxes are taken to be linear in the gradients, is seen to be inaccurate. Even in the case of small artificial changes in density or temperature gradients, changes in the fluxes of different species (''off-diagonal'') generally are significant, or even dominant, compared to those for the same species (''diagonal'').
A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
Wu, Kailiang; Tang, Huazhong; Xiu, Dongbin
2017-09-01
This paper is concerned with generalized polynomial chaos (gPC) approximation for first-order quasilinear hyperbolic systems with uncertainty. The one-dimensional (1D) hyperbolic system is first symmetrized with the aid of left eigenvector matrix of the Jacobian matrix. Then the gPC stochastic Galerkin method is applied to derive a provably symmetrically hyperbolic equations for the gPC expansion coefficients. The resulting deterministic gPC Galerkin system is discretized by a path-conservative finite volume WENO scheme in space and a third-order total variation diminishing Runge-Kutta method in time. The method is further extended to two-dimensional (2D) quasilinear hyperbolic system with uncertainty, where the symmetric hyperbolicity of the one-dimensional gPC Galerkin system is carried over via an operator splitting technique. Several numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed gPC stochastic Galerkin method.
Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith
2017-05-01
In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.
Lee, Jungpyo; Wright, John; Bertelli, Nicola; Jaeger, Erwin F.; Valeo, Ernest; Harvey, Robert; Bonoli, Paul
2017-05-01
In this paper, a reduced model of quasilinear velocity diffusion by a small Larmor radius approximation is derived to couple the Maxwell's equations and the Fokker Planck equation self-consistently for the ion cyclotron range of frequency waves in a tokamak. The reduced model ensures the important properties of the full model by Kennel-Engelmann diffusion, such as diffusion directions, wave polarizations, and H-theorem. The kinetic energy change ( W ˙ ) is used to derive the reduced model diffusion coefficients for the fundamental damping (n = 1) and the second harmonic damping (n = 2) to the lowest order of the finite Larmor radius expansion. The quasilinear diffusion coefficients are implemented in a coupled code (TORIC-CQL3D) with the equivalent reduced model of the dielectric tensor. We also present the simulations of the ITER minority heating scenario, in which the reduced model is verified within the allowable errors from the full model results.
Complementary Lidstone Interpolation and Boundary Value Problems
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Pinelas Sandra
2009-01-01
Full Text Available We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial of degree , which involves interpolating data at the odd-order derivatives. For we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a th order differential equation and the complementary Lidstone boundary conditions.
Sadgrove, M; Parkins, S; Leonhardt, R; Sadgrove, Mark; Mullins, Terry; Parkins, Scott; Leonhardt, Rainer
2004-01-01
We present experimental measurements of the mean energy for the atom optics kicked rotor after just two kicks. The energy is found to deviate from the quasi--linear value for small kicking periods. The observed deviation is explained by recent theoretical results which include the effect of a non--uniform initial momentum distribution, previously applied only to systems using much colder atoms than ours.
KAM for autonomous quasi-linear perturbations of KdV
Baldi, Pietro; Berti, Massimiliano; Montalto, Riccardo
2016-11-01
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear (also called strongly nonlinear) autonomous Hamiltonian differentiable perturbations of the mKdV equation. The proof is based on a weak version of the Birkhoff normal form algorithm and a nonlinear Nash-Moser iteration. The analysis of the linearized operators at each step of the iteration is achieved by pseudo-differential operator techniques and a linear KAM reducibility scheme.
Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear?
Anssari-Benam, Afshin
2014-05-01
The widely popular quasi-linear viscoelasticity (QLV) theory has been employed extensively in the literature for characterising the time-dependent behaviour of many biological tissues, including the aortic valve (AV). However, in contrast to other tissues, application of QLV to AV data has been met with varying success, with studies reporting discrepancies in the values of the associated quantified parameters for data collected from different timescales in experiments. Furthermore, some studies investigating the stress-relaxation phenomenon in valvular tissues have suggested discrete relaxation spectra, as an alternative to the continuous spectrum proposed by the QLV. These indications put forward a more fundamental question: Is the time-dependent behaviour of the aortic valve intrinsically quasi-linear? In other words, can the inherent characteristics of the tissue that govern its biomechanical behaviour facilitate a quasi-linear time-dependent behaviour? This paper attempts to address these questions by presenting a mathematical analysis to derive the expressions for the stress-relaxation G( t) and creep J( t) functions for the AV tissue within the QLV theory. The principal inherent characteristic of the tissue is incorporated into the QLV formulation in the form of the well-established gradual fibre recruitment model, and the corresponding expressions for G( t) and J( t) are derived. The outcomes indicate that the resulting stress-relaxation and creep functions do not appear to voluntarily follow the observed experimental trends reported in previous studies. These results highlight that the time-dependent behaviour of the AV may not be quasi-linear, and more suitable theoretical criteria and models may be required to explain the phenomenon based on tissue's microstructure, and for more accurate estimation of the associated material parameters. In general, these results may further be applicable to other planar soft tissues of the same class, i.e. with the same
Directory of Open Access Journals (Sweden)
Abdelfatah Bouziani
2003-01-01
Full Text Available This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established for the quasilinear problem, using an iterative process based on results obtained for the linear problem.
Anomalous energy exchange in the gBL and quasilinear theories
Mynick, H. E.
1992-05-01
The rate of turbulence-induced energy exchange Ẇ0 between species is computed in the framework of the quasilinear and generalized Balescu-Lenard (gBL) transport theories, and the relationship between these two similar theories is thereby elucidated. For both theories, general formal expressions for Ẇ0 are developed and then applied to the trapped electron mode for illustration. The general expressions for Ẇ0 in the two theories are formally closely related, but can yield predictions of very different magnitude in concrete applications. The fact that quasilinear theory is not valid for saturated steady-state turbulence gives rise to certain peculiarities in its predictions for this normal experimental situation, such as permitting energy to flow from the cooler to the hotter species, even in the limit of thermal equilibrium, where real-space gradients vanish. The gBL theory may be viewed as a modification of quasilinear theory to be valid for steady-state turbulence, keeping extra terms due to the self-consistent back reaction of particles on the fluctuations, which are just such as to eliminate these peculiarities.
拟线性方程非局部边值问题解的衰减估计%Decay Estimates for Solutions to a Quasilinear Nonlocal Boundary Conditions
Institute of Scientific and Technical Information of China (English)
王远弟
2000-01-01
The purpose of this paper is to investigate the decay behavior and dynamics of a quasilinear partial differential equations with nonlocal boundary conditions which is motivated by model problems, arising from quasi-state thermoelasticity, etc.. By constructing an upper solution of the problem, a decay estimate for the solution is obtained.%本文讨论一类源于拟静态热弹性力学和控制理论等领域的边值问题,通过构造适当的上下解得到拟线性方程解的衰减估计.
APPROXIMATE CONTROLLABILITY OF A CLASS OF QUASILINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Wang Chunpeng; Yin Jingxue; Huang Xingbo
2002-01-01
In this paper we study the approximate controllability of a class ofquasilinear parabolic equations in a bounded spacial domain Ω RN when the controlacts on any open and nonempty subset of Ω. The approximate controllability inLp(Ω)for N + 2 ≤ p ＜ +∞ is proved. The proof combines a variational approach to thecontrollability problem for linear equations and a fixed point method.
Quasi-optimal convergence rate of an AFEM for quasi-linear problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2010-01-01
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and D\\"orfler's strategy is assumed for marking. We first prove a contraction property for a suitable definition of total error, which is equivalent to the total error as defined by Casc\\'on et al. (in SIAM J. Numer. Anal. 46 (2008), 2524--2550), and implies line...
Symmetry in an elliptic problem and the blow-up set of a quasilinear heat equation
Energy Technology Data Exchange (ETDEWEB)
Cortazar, C.; Elgueta, M. [Universidad Catolica, Santiago (Chile); Felmer, P. [Universidad de Chile, Santiago (Chile)
1996-12-31
We will consider in this paper a semilinear elliptic equation {triangle}u + f(u) = 0 in {Omega}, (1.5) where the function f is locally Lipschitz in (0,{infinity}) and continuous in (0,{infinity}). We study symmetry properties of nonnegative solutions of this equation in two different situations: first we assume {Omega} = IR{sup N}, and second we consider {Omega} {ne} IR{sup N} and we provide (1.5) with overdetermined boundary conditions. Next we describe our results in the first case, that is, when {Omega} = IR{sup N}. We will consider the following hypothesis on the nonlinear function f (F) f(0) {le} 0, f continuous in (0,+{infinity}), locally Lipschitz in (0,+{infinity}) and there exists {alpha} > 0 so that f is strictly decreasing in [0,{alpha}]. We note that the support of a solution of (1.5) is not known a priori and so we have in fact a free boundary involved. Our goal is to determine the shape of this support and the symmetry properties of the solution.
Quasilinear Elliptic Equations with Neumann Boundary and Singularity
Institute of Scientific and Technical Information of China (English)
Bing-yu Kou; Shuang-jie Peng
2009-01-01
Let Ω be a bounded domain with a smooth C2 boundary in RN(N≥3),0 ∈Ω,and n denote the unit outward normal to aΩ.We are concerned with the Neumann boundary problems:-div(|x|α|△u|p-2△u)=|x|βup(α,β)-1-λ|x|γup-1,u(x)>0,x∈Ω,au/an=0 on aΩ,where 1p,γ>α-p.For various parameters α,β or γ,we establish certain existence results of thesolutions in the case 0 ∈Ω or 0 ∈Ω.
Positive Singular Solutions for Quasilinear Elliptic Equations With Supercritical Growth
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
@@ In this paper we study the existence of positive singular solutions of the following problems div(|(△)u|p-2(△)u)+f(u)=0 in Ω＼{0}(1) limx→0u(x)=∞.(2) Where 1
The Cauchy problem for the Pavlov equation with large data
Wu, Derchyi
2017-08-01
We prove a local solvability of the Cauchy problem for the Pavlov equation with large initial data by the inverse scattering method. The Pavlov equation arises in studies Einstein-Weyl geometries and dispersionless integrable models. Our theory yields a local solvability of Cauchy problems for a quasi-linear wave equation with a characteristic initial hypersurface.
Stability predictions for high-order ΣΔ modulators based on quasilinear modeling
DEFF Research Database (Denmark)
Risbo, Lars
1994-01-01
This paper introduces a novel interpretation of the instability mechanisms in high-order one-bit Sigma-Delta modulators. Furthermore, it is demonstrated how the maximum stable amplitude range can be predicted very well. The results are obtained using an extension of the well known quasilinear mod...... modeling of the one-bit quantizer. The theoretical results are verified by numerical simulations of a number of realistic 4th order modulators designed by means of standard filter design tools. The results are useful for automated design and optimization of loop filters...
Zacharegkas, Georgios; Vlahos, Loukas
2016-01-01
The limitation of the Quasilinear Theory (QLT) to describe the diffusion of electrons and ions in velocity space when interacting with a spectrum of large amplitude electrostatic Langmuir, Upper and Lower hybrid waves, is analyzed. We analytically and numerically estimate the threshold for the amplitude of the waves above which the QLT breaks down, using a test particle code. The evolution of the velocity distribution, the velocity-space diffusion coefficients, the driven current, and the heating of the particles are investigated, for the interaction with small and large amplitude electrostatic waves, i.e. in both regimes, there where QLT is valid and there where it clearly breaks down.
Institute of Scientific and Technical Information of China (English)
Hui Cheng YIN
2001-01-01
For a class of three-dimensional quasilinear wave equations with small initial data, we givea complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjectureposed by John and Hormander. As an application of our result, we show that the solution of three-dimensional isentropic compressible Euler equations with irrotational initial data which are a smallperturbation from a constant state will develop singularity in the first-order derivatives in finite timewhile the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture ofAlinhac.
Oscillation Criteria for Second-Order Quasilinear Neutral Delay Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Guangrong Zhang
2010-01-01
Full Text Available We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations [r(t(zΔ(tγ]Δ+q1(txα(τ1(t+q2(txβ(τ2(t=0 on a time scale 𝕋, where z(t=x(t+p(tx(τ0(t, 0<α<γ<β. Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.
Existence and concentration of positive solutions for a quasilinear elliptic equation in R
Directory of Open Access Journals (Sweden)
Elisandra Gloss
2010-05-01
Full Text Available We study the existence and concentration of positive solutions for the quasilinear elliptic equation $$ -varepsilon^2u'' -varepsilon^2(u^2''u+V(x u = h(u $$ in $mathbb{R}$ as $varepsilono 0$, where the potential $V:mathbb{R}o mathbb{R}$ has a positive infimum and $inf_{partial Omega}V>inf_{ Omega}V$ for some bounded domain $Omega$ in $mathbb{R}$, and $h$ is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.
EXACT CONTROLLABILITY FOR FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEMS WITH VERTICAL CHARACTERISTICS
Institute of Scientific and Technical Information of China (English)
Li Tatsien; Rao Bopeng
2009-01-01
We consider first order quasilinear hyperbolic systems with vertical charac-teristics. It was shown in [4] that such systems can be exactly controllable with the help of internal controls applied to the equations corresponding to zero eigenvalues. However, it is possible that, for physical or engineering reasons, we can not put any control on the equations corresponding to zero eigenvalues. In this paper, we will establish the ex-act controllability only by means of physically meaningful internal controls applied to the equations corresponding to non-zero eigenvalues. We also show the exact controllability for a very simplified model by means of switching controls.
Existence of Nontrivial Weak Solutions to Quasi-Linear Elliptic Equations with Exponential Growth
Institute of Scientific and Technical Information of China (English)
WANG Chong
2013-01-01
In this paper,we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations -△nu+V(x)｜u｜n-2u-f(x,u)/｜x｜β,x∈Rn (n≥2),where-△nu=-div(｜▽u｜n-2▽7u),0≤β ＜ n,V∶ Rn → R is a continuous function,f (x,u)is continuous in Rn × R and behaves like eαun/n-1 as u → +∞.
Systems of Quasilinear Parabolic Equations with Discontinuous Coefficients and Continuous Delays
Directory of Open Access Journals (Sweden)
Tan Qi-Jian
2011-01-01
Full Text Available Abstract This paper is concerned with a weakly coupled system of quasilinear parabolic equations where the coefficients are allowed to be discontinuous and the reaction functions may depend on continuous delays. By the method of upper and lower solutions and the associated monotone iterations and by difference ratios method and various estimates, we obtained the existence and uniqueness of the global piecewise classical solutions under certain conditions including mixed quasimonotone property of reaction functions. Applications are given to three 2-species Volterra-Lotka models with discontinuous coefficients and continuous delays.
Enhancement of residual stress by electromagnetic fluctuations: A quasi-linear study
Kaang, Helen H.; Jhang, Hogun; Singh, R.; Kim, Juhyung; Kim, S. S.
2016-05-01
A study is conducted on the impact of electromagnetic (EM) fluctuations on residual Reynolds stress in the context of the quasi-linear theory. We employ a fluid formulation describing EM ion temperature gradient turbulence. Analyses show that finite plasma β (=plasma thermal energy/magnetic energy) significantly increases the residual stress, potentially leading to the strong enhancement of flow generation in high β plasmas. We identify that this strong increase of residual stress originates from the reinforcement of radial ⟨ k ∥ ⟩ (=spectrally averaged parallel wavenumber) asymmetry due to the deformation of eigenfunctions near a rational surface.
Directory of Open Access Journals (Sweden)
Yekini Shehu
2010-01-01
real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.
Directory of Open Access Journals (Sweden)
Rica Gonen
2013-11-01
Full Text Available We analyze the space of deterministic, dominant-strategy incentive compatible, individually rational and Pareto optimal combinatorial auctions. We examine a model with multidimensional types, nonidentical items, private values and quasilinear preferences for the players with one relaxation; the players are subject to publicly-known budget constraints. We show that the space includes dictatorial mechanisms and that if dictatorial mechanisms are ruled out by a natural anonymity property, then an impossibility of design is revealed. The same impossibility naturally extends to other abstract mechanisms with an arbitrary outcome set if one maintains the original assumptions of players with quasilinear utilities, public budgets and nonnegative prices.
Quasi-linear wave-particle interactions in the earth's radiation belts
Villalon, Elena; Silevitch, Michel B.; Rothwell, Paul L.; Burke, William J.
1989-11-01
A self-consistent theory on the interaction of magnetospheric particles with ducted electromagnetic cyclotron waves is presented. The main contribution is to calculate the coupling coefficients for the ray equations describing the temporal evolution of the cyclotron instability. These are obtained within the framework of quasi-linear interaction of waves and particles. A set of equations is derived based on the Fokker-Planck theory of pitch angle diffusion, describing the evolution time of the number of particles in the flux tube and the energy density of waves for the interaction of Alfven waves with protons and of whistler waves with electrons. The coupling coefficients are obtained, based on a quasi-linear analysis after averaging over the particle bounce motion. It is found that the equilibrium solutions for particle fluxes and wave amplitudes are stable under small local perturbations. The reflection of the waves in the ionosphere is discussed. A stability analysis around the equilibrium solutions for precipitating particle fluxes and wave intensity indicates that an actively excited ionosphere can cause the development of explosive instabilities.
Conservation Laws, Hodograph Transformation and Boundary Value Problems of Plane Plasticity
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Sergey I. Senashov
2012-10-01
Full Text Available For the hyperbolic system of quasilinear first-order partial differential equations, linearizable by hodograph transformation, the conservation laws are used to solve the Cauchy problem. The equivalence of the initial problem for quasilinear system and the problem for conservation laws system permits to construct the characteristic lines in domains, where Jacobian of hodograph transformations is equal to zero. Moreover, the conservation laws give all solutions of the linearized system. Some examples from the gas dynamics and theory of plasticity are considered.
Lipschitz Properties in Variable Exponent Problems via Relative Rearrangement
Institute of Scientific and Technical Information of China (English)
Jean-Michel RAKOTOSON
2010-01-01
The author first studies the Lipschitz properties of the monotone and relative rearrangement mappings in variable exponent Lebesgue spaces completing the result given in[9].This paper is ended by establishing the Lipschitz properties for quasilinear problems with variable exponent when the right-hand side is in some dual spaces of a suitable Sobolev space associated to variable exponent.
Quasi-linear vacancy dynamics modeling and circuit analysis of the bipolar memristor.
Abraham, Isaac
2014-01-01
The quasi-linear transport equation is investigated for modeling the bipolar memory resistor. The solution accommodates vacancy and circuit level perspectives on memristance. For the first time in literature the component resistors that constitute the contemporary dual variable resistor circuit model are quantified using vacancy parameters and derived from a governing partial differential equation. The model describes known memristor dynamics even as it generates new insight about vacancy migration, bottlenecks to switching speed and elucidates subtle relationships between switching resistance range and device parameters. The model is shown to comply with Chua's generalized equations for the memristor. Independent experimental results are used throughout, to validate the insights obtained from the model. The paper concludes by implementing a memristor-capacitor filter and compares its performance to a reference resistor-capacitor filter to demonstrate that the model is usable for practical circuit analysis.
Modelling and Quasilinear Control of Compressor Surge and Rotating Stall Vibrations
Directory of Open Access Journals (Sweden)
Ranjan Vepa
2010-01-01
Full Text Available An unsteady nonlinear and extended version of the Moore-Greitzer model is developed to facilitate the synthesis of a quasilinear stall vibration controller. The controller is synthesised in two steps. The first step defines the equilibrium point and ensures that the desired equilibrium point is stable. In the second step, the margin of stability at the equilibrium point is tuned or increased by an appropriate feedback of change in the mass flow rate about the steady mass flow rate at the compressor exit. The relatively simple and systematic non-linear modelling and linear controller synthesis approach adopted in this paper clearly highlights the main features on the controller that is capable of inhibiting compressor surge and rotating stall vibrations. Moreover, the method can be adopted for any axial compressor provided its steady-state compressor and throttle maps are known.
EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT
Institute of Scientific and Technical Information of China (English)
康东升
2004-01-01
This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s ＜ p, 1 ＜ p ＜ N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ＞ 0,p ≤ r ＜ p* ,p* := Np/N-p is the critical Sobolev exponent, μ＞ 0, 0 ≤ t ＜ p, p ≤ q ＜ p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.
Quasilinear theory of Fermi acceleration in a multicusp magnetic confinement geometry
Dewar, R L; Dewar, Robert L.; Ciubotariu, Carmen I.
1999-01-01
Particle motion in a cylindrical multiple-cusp magnetic field configuration is shown to be highly, but not completely, chaotic (cf. a Sinai billiard). Analysis of the dynamics of the reflection process shows that the great majority of particles reflect nonadiabatically, unlike the case in a magnetic mirror. A quasilinear theory of diffusion is developed for particles with a Hamiltonian of the form $H_0+H_1$, where $H_0$ is a nonintegrable unperturbed Hamiltonian (e.g. particle in a multicusp field) giving rise to chaotic dynamics, while the perturbation $H_1$ is coherent (e.g. electromagnetic wave). For the multicusp geometry, two heating mechanisms are identified --- cyclotron resonance heating of particles temporarily mirror-trapped in the cusps, and nonresonant heating of the nonadiabatically reflected particles. An analytically solvable model leads to an expression for a transit-time correction factor, exponentially decreasing with increasing frequency. The theory is illustrated with parameters from a typ...
Quasilinear theory of collisionless Fermi acceleration in a multicusp magnetic confinement geometry
Dewar, R. L.; Ciubotariu, C. I.
1999-12-01
Particle motion in a cylindrical multiple-cusp magnetic field configuration is shown to be highly (though not completely) chaotic, as expected by analogy with the Sinai billiard. This provides a collisionless, linear mechanism for phase randomization during monochromatic wave heating. A general quasilinear theory of collisionless energy diffusion is developed for particles with a Hamiltonian of the form H0+H1, motion in the unperturbed Hamiltonian H0 being assumed chaotic, while the perturbation H1 can be coherent (i.e., not stochastic). For the multicusp geometry, two heating mechanisms are identified-cyclotron resonance heating of particles temporarily mirrortrapped in the cusps, and nonresonant heating of nonadiabatically reflected particles (the majority). An analytically solvable model leads to an expression for a transit-time correction factor, exponentially decreasing with increasing frequency. The theory is illustrated using the geometry of a typical laboratory experiment.
Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics
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O. A. Pokhotelov
2010-12-01
Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.
A quasi-linear analysis of the impurity effect on turbulent momentum transport and residual stress
Ko, S H; Singh, R
2015-01-01
We study the impact of impurities on turbulence driven intrinsic rotation (via residual stress) in the context of the quasi-linear theory. A two-fluid formulation for main and impurity ions is employed to study ion temperature gradient modes in sheared slab geometry modified by the presence of impurities. An effective form of the parallel Reynolds stress is derived in the center of mass frame of a coupled main ion-impurity system. Analyses show that the contents and the radial profile of impurities have a strong influence on the residual stress. In particular, an impurity profile aligned with that of main ions is shown to cause a considerable reduction of the residual stress, which may lead to the reduction of turbulence driven intrinsic rotation.
Strong global attractor for a quasilinear nonlocal wave equation on $mathbb{R}^N$
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Perikles G. Papadopoulos
2006-07-01
Full Text Available We study the long time behavior of solutions to the nonlocal quasilinear dissipative wave equation $$ u_{tt}-phi (x| abla u(t|^{2}Delta u+delta u_{t}+|u|^{a}u=0, $$ in $mathbb{R}^N$, $t geq 0$, with initial conditions $ u(x,0 = u_0 (x$ and $u_t(x,0 = u_1(x$. We consider the case $N geq 3$, $delta> 0$, and $(phi (x^{-1}$ a positive function in $L^{N/2}(mathbb{R}^Ncap L^{infty}(mathbb{R}^N $. The existence of a global attractor is proved in the strong topology of the space $mathcal{D}^{1,2}(mathbb{R}^N imes L^{2}_{g}(mathbb{R}^N$.
Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process
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Dazi Li
2015-01-01
Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.
Guttenfelder, W.; Kaye, S. M.; Ren, Y.; Solomon, W.; Bell, R. E.; Candy, J.; Gerhardt, S. P.; LeBlanc, B. P.; Yuh, H.
2016-05-01
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas, profiles are most unstable to microtearing modes that are only effective in transporting electron energy. However, sub-dominant electromagnetic and electrostatic ballooning modes are also unstable, which are effective at transporting energy, particles, and momentum. The quasi-linear prediction of transport from these weaker ballooning modes, assuming they contribute transport in addition to that from microtearing modes in a nonlinear turbulent state, leads to a very small or outward convection of momentum, inconsistent with the experimentally measured inward pinch, and opposite to predictions in conventional aspect ratio tokamaks. Additional predictions of a low beta L-mode plasma, unstable to more traditional electrostatic ion temperature gradient-trapped electron mode instability, show that the Coriolis pinch is inward but remains relatively weak and insensitive to many parameter variations. The weak or outward pinch predicted in NSTX plasmas appears to be at least partially correlated to changes in the parallel mode structure that occur at a finite beta and low aspect ratio, as discussed in previous theories. The only conditions identified where a stronger inward pinch is predicted occur either in the purely electrostatic limit or if the aspect ratio is increased. As the Coriolis pinch cannot explain the measured momentum pinch, additional theoretical momentum transport mechanisms are discussed that may be potentially important.
The clustering of dark matter haloes: scale-dependent bias on quasi-linear scales
Jose, Charles; Lacey, Cedric G.; Baugh, Carlton M.
2016-11-01
We investigate the spatial clustering of dark matter haloes, collapsing from 1σ-4σ fluctuations, in the redshift range 0-5 using N-body simulations. The halo bias of high redshift haloes (z ≥ 2) is found to be strongly nonlinear and scale dependent on quasi-linear scales that are larger than their virial radii (0.5-10 Mpc h-1). However, at lower redshifts, the scale dependence of nonlinear bias is weaker and is of the order of a few per cent on quasi-linear scales at z ˜ 0. We find that the redshift evolution of the scale-dependent bias of dark matter haloes can be expressed as a function of four physical parameters: the peak height of haloes, the nonlinear matter correlation function at the scale of interest, an effective power-law index of the rms linear density fluctuations and the matter density of the universe at the given redshift. This suggests that the scale dependence of halo bias is not a universal function of the dark matter power spectrum, which is commonly assumed. We provide a fitting function for the scale-dependent halo bias as a function of these four parameters. Our fit reproduces the simulation results to an accuracy of better than 4 per cent over the redshift range 0 ≤ z ≤ 5. We also extend our model by expressing the nonlinear bias as a function of the linear matter correlation function. It is important to incorporate our results into the clustering models of dark matter haloes at any redshift, including those hosting early generations of stars and galaxies before reionization.
Kumar, Bipin; Das, Apurba; Alagirusamy, R
2012-09-01
Understanding the stress relaxation behavior of the compression bandage could be very useful in determining the behavior of the interface pressure exerted by the bandage on a limb during the course of the compression treatment. There has been no comprehensive study in the literature to investigate the pressure profile (interface pressure with time) generated by a compression bandage when applied at different levels of strain. The present study attempts to describe the pressure profile, with the use of a quasi-linear viscoelastic model, generated by a compression bandage during compression therapy. The quasi-linear viscoelastic (QLV) theory proposed by Fung (Fung, 1972, "Stress Strain History Relations of Soft Tissues in Simple Elongation," Biomechanics: Its Foundations and Objectives, Y. C. Fung, N. Perrone, and M. Anliker, eds., Prentice-Hall, Englewood Cliffs, NJ, pp. 181-207). was used to model the nonlinear time- and history-dependent relaxation behavior of the bandage using the ramp strain approach. The regression analysis was done to find the correlation between the pressure profile and the relaxation behavior of the bandage. The parameters of the QLV model, describing the relaxation behavior of the bandage, were used to determine the pressure profile generated by the bandage at different levels of strain. The relaxation behaviors of the bandage at different levels of strain were well described by the QLV model parameters. A high correlation coefficient (nearly 0.98) shows a good correlation of the pressure profile with the stress relaxation behavior of the bandage.The prediction of the pressure profile using the QLV model parameters were in agreement with the experimental data. The pressure profile generated by a compression bandage could be predicted using the QLV model describing the nonlinear relaxation behavior of the bandage. This new application of the QLV theory helps in evaluating the bandage performance during compression therapy as scientific wound
Nonuniqueness of solutions of initial-value problems for parabolic p-Laplacian
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Jiri Benedikt
2015-02-01
Full Text Available We construct a positive solution to a quasilinear parabolic problem in a bounded spatial domain with the p-Laplacian and a nonsmooth reaction function. We obtain nonuniqueness for zero initial data. Our method is based on sub- and supersolutions and the weak comparison principle. Using the method of sub- and supersolutions we construct a positive solution to a quasilinear parabolic problem with the p-Laplacian and a reaction function that is non-Lipschitz on a part of the spatial domain. Thereby we obtain nonuniqueness for zero initial data.
März, Thomas
2010-01-01
Here we study the Dirichlet problem for first order linear and quasi-linear hyperbolic PDEs on a simply connected bounded domain of $\\R^2$, where the domain has an interior outflow set and a mere inflow boundary. By means of a Lyapunov function we show the existence of a unique solution in the space of functions of bounded variation and its continuous dependence on all the data of the linear problem. Finally, we conclude the existence of a solution to the quasi-linear case by utilizing the Schauder fixed point theorem. This type of problems considered here appears in applications such as transport based image inpainting.
Energy Technology Data Exchange (ETDEWEB)
Rax, J.M.
1992-04-01
The dynamics of electrons in two-dimensional, linearly or circularly polarized, ultra-high intensity (above 10{sup 18}W/cm{sup 2}) laser waves, is investigated. The Compton harmonic resonances are identified as the source of various stochastic instabilities. Both Arnold diffusion and resonance overlap are considered. The quasilinear kinetic equation, describing the evolution of the electron distribution function, is derived, and the associated collisionless damping coefficient is calculated. The implications of these new processes are considered and discussed.
Institute of Scientific and Technical Information of China (English)
Dao Yuan FANG; Ru Ying XUE
2006-01-01
In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption.
Why is the force-velocity relationship in leg press tasks quasi-linear rather than hyperbolic?
Bobbert, Maarten F
2012-06-01
Force-velocity relationships reported in the literature for functional tasks involving a combination of joint rotations tend to be quasi-linear. The purpose of this study was to explain why they are not hyperbolic, like Hill's relationship. For this purpose, a leg press task was simulated with a musculoskeletal model of the human leg, which had stimulation of knee extensor muscles as only independent input. In the task the ankles moved linearly, away from the hips, against an imposed external force that was reduced over contractions from 95 to 5% of the maximum isometric value. Contractions started at 70% of leg length, and force and velocity values were extracted when 80% of leg length was reached. It was shown that the relationship between leg extension velocity and external force was quasi-linear, while the relationship between leg extension velocity and muscle force was hyperbolic. The discrepancy was explained by the fact that segmental dynamics canceled more and more of the muscle force as the external force was further reduced and velocity became higher. External power output peaked when the imposed external force was ∼50% of maximum, while muscle power output peaked when the imposed force was only ∼15% of maximum; in the latter case ∼70% of muscle power was buffered by the leg segments. According to the results of this study, there is no need to appeal to neural mechanisms to explain why, in leg press tasks, the force-velocity relationship is quasi-linear rather than hyperbolic.
Li, Wanli; Qie, Xiushu; Fu, Shenming; Su, Debin; Shen, Yonghai
2016-01-01
Two intense quasi-linear mesoscale convective systems (QLMCSs) in northern China were simulated using the WRF (Weather Research and Forecasting) model and the 3D-Var (three-dimensional variational) analysis system of the ARPS (Advanced Regional Prediction System) model. A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures. Results indicate that, compared with calculating the results using two previous methods, the lightning density calculated using the new method presented in this study is in better accordance with observations. Based on the calculated lightning densities using the new method, it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs, where the surface wind field converged intensely. The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it, and their lightning events mainly occurred in regions with a large gradient of CAPE. Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions; the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different; and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.
Global existence and boundedness in a higher-dimensional quasilinear chemotaxis system
Wang, Yilong; Xiang, Zhaoyin
2015-12-01
This paper deals with the boundedness of global solutions to the quasilinear Keller-Segel system u_t=nabla\\cdotbig(D(u)nabla u-unabla vbig), &quad xinΩ, t>0, v_t=Δ v-uf(v),&quad xinΩ, t>0, nabla u\\cdot ν=0, nabla v\\cdotν=0,&quad xin partialΩ, t>0 in a bounded domain {Ωsubset Rn(n≥ 3)} with smooth boundary, where D( u) is supposed to satisfy D( u) ≥ D 0 u m-1 with some positive constant D 0. It is proved that when {m>2-n+2/2n}, the system possesses global bounded weak solutions for any sufficiently smooth nonnegative initial data. In particular, we improved the recent result by Wang et al. (Z Angew Math Phys, 2015. doi: 10.1007/s00033-014-0491-9 ) in the sense that we established the global boundedness of weak solutions. We also removed the convexity assumption on the domain used by Wang et al. (Z Angew Math Phys 65:1137-1152, 2014, 2015).
Wang, Wei; Ding, Mengyao; Li, Yan
2017-09-01
In this paper we study the global boundedness of solutions to the quasilinear parabolic chemotaxis system: ut = ∇ ṡ (D (u) ∇u - S (u) ∇φ (v)), 0 = Δv - v + u, subject to homogeneous Neumann boundary conditions and the initial data u0 in a bounded and smooth domain Ω ⊂Rn (n ≥ 2), where the diffusivity D (u) is supposed to satisfy D (u) ≥a0(u + 1) - α with a0 > 0 and α ∈ R, while the density-signal governed sensitivity fulfills 0 ≤ S (u) ≤b0(u + 1) β and 0 0 and β , k ∈ R. It is shown that the solution is globally bounded if α + β benefits the global boundedness of solutions due to the weaker chemotactic migration of the signal-dependent sensitivity at high signal concentrations. Moreover, when α + β arrives at the critical value, we establish the global boundedness of solutions for the coefficient χ properly small. It should be emphasized that the smallness of χ under k > 1 is positively related to the total cellular mass ∫Ωu0 dx, which is attributed to the stronger singularity of φ (v) at v = 0 for k > 1 and the fact that v can be estimated from below by a multiple of ∫Ωu0 dx. In addition, distinctive phenomena concerning this model are observed by comparison with the known results.
Quasi-linear analysis of ion Weibel instability in the earth's neutral sheet
Lui, Anthony T. Y.; Yoon, Peter H.; Chang, Chia-Lie
1993-01-01
A quasi-linear analysis of the ion Weibel instability (IWI) for waves with parallel propagation is carried out for parameters appropriate to the earth's neutral sheet during the substorm interval. For ion drift speed reaching sizable fraction of the ion thermal speed, unstable waves grow to a nonlinear regime in a time interval greater than an ion gyroperiod. The saturation level is attained with current density reduced to about 15-28 percent of its preactivity level. The unstable wave amplitude normalized to the initial ambient field is found to be in the range of 0.2-0.8. This is accompanied by ion heating along the magnetic field with the parallel temperature being enhanced by 25-90 percent. Thus, the IWI can provide nonadiabatic heating of ions in current disruptions during substorms. The associated anomalous resistivity is estimated to be about 1 x 10 exp -7 to 1 x 10 exp -6 s, which is about 11 to 12 orders of magnitude above the classical resistivity.
Complementary Lidstone Interpolation and Boundary Value Problems
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Ravi P. Agarwal
2009-01-01
Full Text Available We shall introduce and construct explicitly the complementary Lidstone interpolating polynomial P2m(t of degree 2m, which involves interpolating data at the odd-order derivatives. For P2m(t we will provide explicit representation of the error function, best possible error inequalities, best possible criterion for the convergence of complementary Lidstone series, and a quadrature formula with best possible error bound. Then, these results will be used to establish existence and uniqueness criteria, and the convergence of Picard's, approximate Picard's, quasilinearization, and approximate quasilinearization iterative methods for the complementary Lidstone boundary value problems which consist of a (2m+1th order differential equation and the complementary Lidstone boundary conditions.
Some problems on nonlinear hyperbolic equations and applications
Peng, YueJun
2010-01-01
This volume is composed of two parts: Mathematical and Numerical Analysis for Strongly Nonlinear Plasma Models and Exact Controllability and Observability for Quasilinear Hyperbolic Systems and Applications. It presents recent progress and results obtained in the domains related to both subjects without attaching much importance to the details of proofs but rather to difficulties encountered, to open problems and possible ways to be exploited. It will be very useful for promoting further study on some important problems in the future.
A STABILITY THEOREM FOR CONSTRAINED OPTIMAL CONTROL PROBLEMS
Institute of Scientific and Technical Information of China (English)
M.H. Farag
2004-01-01
This paper presents the stability of difference approximations of an optimal control problem for a quasilinear parabolic equation with controls in the coefficients, boundary conditions and additional restrictions. The optimal control problem has been convered to one of the optimization problem using a penalty function technique. The difference approximations problem for the considered problem is obtained. The estimations of stability of the solution of difference approximations problem are proved. The stability estimation of the solution of difference approximations problem by the controls is obtained.
Classical implicit travelling wave solutions for a quasilinear convection-diffusion equation
Hearns, Jessica; Van Gorder, Robert A.
2012-11-01
We discuss classical implicit solutions to the partial differential equation ut=(H(u))xx+(G(u))x, a general convection-diffusion PDE with particular subcases appearing in many areas of fluids and astrophysics. As an illustrative example, and to compare our results with those present in the literature, we frequently consider travelling wave solutions for the quasilinear PDE ut=(um)xx+(un)x, which has been used to describe the flow of viscous fluids on an inclined bed and as a model of convection-diffusion processes. When n ⩾ m > 1, this equation can be used to model the flow of a fluid under gravity through a homogeneous and isotropic porous medium. The travelling wave ODE for both the general and more specific cases have a first integral which is used to obtain an implicit solution for the travelling wave profiles. We should mention that, for some values of m, the implicit relation can be solved in closed form for explicit exact solutions. In the case of n = 2m - 1, solving the implicit relation gives a general way of obtaining the solutions found in Vanaja [Vanaja, V., 2009. Physica Scripta 80, p. 045402] where the travelling wave solutions for the cases (m, n) = (2, 3) and (m, n) = (3, 5) were explicitly constructed using a more complicated ansatz method. For other more complicated cases where inversion cannot be performed, we apply the method of series reversion to construct series solutions from the implicit relations. Furthermore, we deduce the dependence of travelling wave solutions on the wave speed, even in cases where the explicit exact solution cannot be found.
Quasi-linear modeling of lower hybrid current drive in ITER and DEMO
Energy Technology Data Exchange (ETDEWEB)
Cardinali, A., E-mail: alessandro.cardinali@enea.it; Cesario, R.; Panaccione, L.; Santini, F.; Amicucci, L.; Castaldo, C.; Ceccuzzi, S.; Mirizzi, F.; Tuccillo, A. A. [ENEA, Unità Tecnica Fusione, Via E Fermi 45 Rome (Italy)
2015-12-10
First pass absorption of the Lower Hybrid waves in thermonuclear devices like ITER and DEMO is modeled by coupling the ray tracing equations with the quasi-linear evolution of the electron distribution function in 2D velocity space. As usually assumed, the Lower Hybrid Current Drive is not effective in a plasma of a tokamak fusion reactor, owing to the accessibility condition which, depending on the density, restricts the parallel wavenumber to values greater than n{sub ∥crit} and, at the same time, to the high electron temperature that would enhance the wave absorption and then restricts the RF power deposition to the very periphery of the plasma column (near the separatrix). In this work, by extensively using the “ray{sup star}” code, a parametric study of the propagation and absorption of the LH wave as function of the coupled wave spectrum (as its width, and peak value), has been performed very accurately. Such a careful investigation aims at controlling the power deposition layer possibly in the external half radius of the plasma, thus providing a valuable aid to the solution of how to control the plasma current profile in a toroidal magnetic configuration, and how to help the suppression of MHD mode that can develop in the outer part of the plasma. This analysis is useful not only for exploring the possibility of profile control of a pulsed operation reactor as well as the tearing mode stabilization, but also in order to reconsider the feasibility of steady state regime for DEMO.
Quasi-linear wave-particle interactions in the Earth's radiation belts
Energy Technology Data Exchange (ETDEWEB)
Villalon, E. (Center for Electromagnetics Research, Northeastern University, Boston, Massachusetts (USA)); Burke, W.J.; Rothwell, P.L. (Air Force Geophysics Laboratory, Hanscom Air Force Base, Massachusetts (USA)); Silevitch, M.B. (Center for Electromagnetic Research, Northeastern University, Boston, Massachusetts (USA))
1989-11-01
This paper studies the theory of gyroresonant interactions of energetic trapped electrons and protons in the Earth's radiation zones with ducted electromagnetic cyclotron waves. Substorm injected electrons in the mid-latitude regions interact with coherent VLF signals, such as whistler mode waves. Energetic protons may interact with narrow-band hydromagnetic (Alfven) waves. A set of equations is derived based on the Fokker-Planck theory of pitch angle diffusion. They describe the evolution in time of the number of particles in the flux tube and the energy density of waves, for the interaction of Alfven waves with protons and of whistler waves with electrons. The coupling coefficients are obtained based on a quasi-linear analysis after averaging over the particle bounce motion. It is found that the equilibrium solutions for particle fluxes and wave amplitudes are stable under small local perturbations. The reflection of the waves in the ionosphere is discussed. To efficiently dump the energetic particles from the radiation belts, the reflection coefficient must be very close to unity so waves amplitudes can grow to high values. Then, the precipitating particle fluxes may act as a positive feedback to raise the height integrated conductivity of the ionosphere which in turn, enhances the reflection of the waves. In addition, by heating the foot of the flux tube with high intensity, RF energy the mirroring properties of the ionosphere are also enhanced. The stability analysis around the equilibrium solutions for precipitating particle fluxes and wave intensity show that an actively excited ionosphere can cause the development of explosive instabilities. {copyright} American Geophysical Union 1989
Quasi-linear viscoelastic properties of the human medial patello-femoral ligament.
Criscenti, G; De Maria, C; Sebastiani, E; Tei, M; Placella, G; Speziali, A; Vozzi, G; Cerulli, G
2015-12-16
The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament.
ON THE NONLINEAR RIEMANN PROBLEMS FOR GENERAL FIRST ELLIPTIC SYSTEMS IN THE PLANE
Institute of Scientific and Technical Information of China (English)
李明忠; 宋洁
2005-01-01
The nonlinear Riemann problem for general systems of the first-order linear and quasi-linear equations in the plane are considered. It translates them to singular integral equations and proves the existence of the solution by means of contract principle or. general contract principle. The known results are generalized.
Energy Technology Data Exchange (ETDEWEB)
Fuentes, Carlos [Instituto Mexicano de Tecnologia del Agua, Jiutepec, Morelos (Mexico); Parlangue, Jean-Yves [Departamento de Agricultura e Ingenieria Biologica (United States); Haverkamp, Randel; Vauclin, Michael [Laboratorio de Estudio de las Transferencias en Hidrologia y Medio ambiente (France)
2001-12-01
The exact solution of the one-dimensional vertical infiltration equation is deducted, when the hydraulic diffusivity is considered constant and the hydraulic conductivity is a combination of both a linear and quadratic functions of the soil water content. This quasi-linear solution includes as particular cases, both the classical solution known as linear soil and the Knight solution. The cumulative infiltrated water as a function of time provided by the quasi-linear solution has been compared with the cumulative infiltrated water obtained from the numerical solution of the Richards equation on three different soils of contrasting hydrodynamic properties. The good agreement between the two solutions has shown that the quasi-linear solution can be used on soils where the accepted hypothesis, on hydraulic diffusivity and hydraulic conductivity, for its deduction is not satisfied. [Spanish] Se deduce la solucion exacta de la ecuacion de la infiltracion unidimensional vertical cuando la difusividad hidraulica es considerada constante y la conductividad hidraulica es una combinacion de una funcion lineal y una cuadratica del contenido volumetrico de agua. Esta solucion cuasi-lineal de la infiltracion contiene, como casos particulares, la solucion clasica conocida como suelo lineal y la solucion de Knight. La lamina infiltrada acumulada en funcion del tiempo proporcionada por la solucion cuasi-lineal se ha comparado con la lamina infiltrada proporcionada por la solucion numerica de la ecuacion de Richards en tres suelos de propiedades hidrodinamicas contrastantes. El buen acuerdo entre las laminas infiltradas ha mostrado que la solucion cuasi-lineal puede utilizarse en suelos donde la difusividad y la conductividad hidraulicas no satisfacen los supuestos de la deduccion.
Energy Technology Data Exchange (ETDEWEB)
Rax, J.M. (Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08540 (United States))
1992-12-01
The dynamics of an electron in a finite set of linearly or circularly polarized ultra-high-intensity (above 10{sup 18} W/cm{sup 2}) laser waves is investigated within the framework of a Hamiltonian analysis. The Compton harmonic resonances are identified as the source of various stochastic instabilities. The stochasticity threshold due to resonance overlap is calculated and the structure of the resonances is analyzed. The quasilinear kinetic equation describing the evolution of the electron distribution function is derived, and the associated collisionless damping coefficient is calculated. The implications of these new processes are considered and discussed.
Zhang, Debing; Xu, Yingfeng; Wang, Shaojie
2017-08-01
The quasilinear transport fluxes due to the ion temperature gradient instability are calculated in a toroidal plasma, in which the magnetic drift resonance is treated rigorously. The effects of the equilibrium parallel flow and flow shear on the radial particle and heat fluxes are studied numerically in detail. In the radial component of parallel viscosity, there exist the pinches driven by the density gradient, the temperature gradient, and the curvature of the background magnetic field. The direction of these pinches is discussed. It is found that each pinch can be inward or outward, which depends crucially on the resonance condition.
Wen, Zijuan; Fan, Meng; Asiri, Asim M; Alzahrani, Ebraheem O; El-Dessoky, Mohamed M; Kuang, Yang
2017-04-01
This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.
Bates, R C; Frey, D D
1998-07-24
Chromatofocusing utilizes internally generate, retained pH gradients to focus proteins into narrow chromatographic bands. One of the characteristics of current chromatofocusing methods is that they use expensive polyampholyte buffers containing large numbers of ill-defined components in order to generate linear or quasi-linear pH gradients. In addition to being costly to use, polyampholyte buffers also tend to associate with proteins and often yield irreproducible gradient shapes. In order to avoid the various difficulties associated with the use of polyampholyte buffers, this study investigates the use of mixtures of simple buffering species to generate quasi-linear pH gradients on a weak-base ion-exchange column packing. The ability of these gradients to separate protein mixtures was also investigated. To optimize the conditions used, a computer simulation method using a local equilibrium model developed that predicts the shape of the pH gradient. Several experiments were performed that demonstrate the usefulness of the method and the accuracy of the model.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
Bouse, E
2010-01-01
We consider systems where a cycle born via the Hopf bifurcation blows up to infinity as a parameter ranges over a finite interval. Two examples demonstrating this effect are presented: planar Lotka-Volterra type systems with a competition-cooperation term and quasi-linear higher order equations.
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-08-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Uniqueness of a positive solution for quasilinear elliptic equations in Heisenberg group
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Kaushik Bal
2016-06-01
Full Text Available In this note we address the question of uniqueness of the Brezis-Oswald problem for the p-Laplacian operator in Heisenberg Group. The non-availability of $C^{1,\\alpha}$ regularity for all $1
problem to extend the proof of Diaz-Saa [10] in the Heisenberg Group case. We overcome the problem by proving directly a generalized version of Diaz-Saa inequality in the Heisenberg Group.
Numerical methods for solving terminal optimal control problems
Gornov, A. Yu.; Tyatyushkin, A. I.; Finkelstein, E. A.
2016-02-01
Numerical methods for solving optimal control problems with equality constraints at the right end of the trajectory are discussed. Algorithms for optimal control search are proposed that are based on the multimethod technique for finding an approximate solution of prescribed accuracy that satisfies terminal conditions. High accuracy is achieved by applying a second-order method analogous to Newton's method or Bellman's quasilinearization method. In the solution of problems with direct control constraints, the variation of the control is computed using a finite-dimensional approximation of an auxiliary problem, which is solved by applying linear programming methods.
Bifurcation from infinity and nodal solutions of quasilinear elliptic differential equations
Directory of Open Access Journals (Sweden)
Bian-Xia Yang
2014-01-01
Full Text Available In this article, we establish a unilateral global bifurcation theorem from infinity for a class of $N$-dimensional p-Laplacian problems. As an application, we study the global behavior of the components of nodal solutions of the problem $$\\displaylines{ \\operatorname{div}(\\varphi_p(\
Institute of Scientific and Technical Information of China (English)
罗李平
2007-01-01
In this paper, oscillatory properties for solutions of the systems of certain quasilinear impulsive delay hyperbolic equations with nonlinear diffusion coefficient are investigated. A sufficient criterion for oscillations of such systems is obtained.
Institute of Scientific and Technical Information of China (English)
Zhang Peixin
2007-01-01
In this paper the existence and nonexistence of non-trivial solution for the Cauchy problem of the form ｛ut=div(｜▽u｜p-2▽u)-(σ)/(σ)xibi(u)-uq,u(x,O)=O,(x,t)∈ST=RN×(O,T),x∈RN\\｛O｝are studied. We assume that ｜b'i(s)｜≤Msm-1, and proved that if P＞2, 0＜q＜p-1+p/N,0≤m＜p-1+p/N, then the problem has a solution;if p＞2, q＞p-1+p/N,O≤m≤q(p+Np-N-1)/p+Np-N, then the problem has no solution;if p＞2,p-1＜q＜p-1+p/N,0≤m＜q, then the problem has a very singular solution;if p＞2,q＞p-1+p/N, 0＜m＜q-p/2N,then the problem has no very singular solution.We use P.D.E.methods such as regularization,Moser iteration and Imbedding Theorem.
Contrast structures for a quasilinear Sobolev-type equation with unbalanced nonlinearity
Bykov, A. A.; Nefedov, N. N.; Sharlo, A. S.
2014-08-01
The existence of a solution to a generalized Kolmogorov-Petrovskii-Piskunov equation is proved and its asymptotic expansion of the internal transition layer type is constructed. The convergence of the asymptotics is proved by applying the asymptotic comparison principle developed for a new class of problems.
Waltz, R. E.; Ferraro, N. M.
2015-04-01
The linear response profiles for the 3D perturbed magnetic fields, currents, ion velocities, plasma density, pressures, and electric potential from low-n external resonant magnetic field perturbations (RMPs) are obtained from the collisional two-fluid M3D-C1 code [N. M. Ferraro and S. C. Jardin, J. Comput. Phys. 228, 7742 (2009)]. A newly developed post-processing RMPtran code computes the resulting quasilinear E×B and magnetic (J×B) radial transport flows with respect to the unperturbed flux surfaces in all channels. RMPtran simulations focus on ion (center of mass) particle and transient non-ambipolar current flows, as well as the toroidal angular momentum flow. The paper attempts to delineate the RMP transport mechanisms that might be responsible for the RMP density pump-out seen in DIII-D [M. A. Mahdavi and J. L. Luxon, Fusion Sci. Technol. 48, 2 (2005)]. Experimentally, the starting high toroidal rotation does not brake to a significantly lower rotation after the pump-out suggesting that convective and E×B transport mechanisms dominate. The direct J×B torque from the transient non-ambipolar radial current expected to accelerate plasma rotation is shown to cancel much of the Maxwell stress J×B torque expected to brake the plasma rotation. The dominant E×B Reynolds stress accelerates rotation at the top of the pedestal while braking rotation further down the pedestal.
Institute of Scientific and Technical Information of China (English)
Li Ta-tsien(李大潜); Peng Yue-Jun
2003-01-01
Abstract We prove that the C0 boundedness of solution impliesthe global existence and uniqueness of C1 solution to the initial-boundary value problem for linearly degenerate quasilinear hyperbolic systems of diagonal form with nonlinear boundary conditions. Thus, if the C1 solution to the initial-boundary value problem blows up in a finite time, then the solution itself must tend to the infinity at the starting point of singularity.
Properties of positive solutions to a nonlinear parabolic problem
Institute of Scientific and Technical Information of China (English)
2007-01-01
This paper deals with the properties of positive solutions to a quasilinear parabolic equation with the nonlinear absorption and the boundary flux. The necessary and sufficient conditions on the global existence of solutions are described in terms of different parameters appearing in this problem. Moreover, by a result of Chasseign and Vazquez and the comparison principle, we deduce that the blow-up occurs only on the boundary (?)Ω. In addition, for a bounded Lipschitz domainΩ, we establish the blow-up rate estimates for the positive solution to this problem with a= 0.
Lyahov, Vladimir; Neshchadim, Vladimir
2015-04-01
Investigation of the stability nonelectroneutral current sheets in the linear approximation [1-4] gives information only on the initial stage of development of perturbations when their amplitudes are small. Within the framework of the quasi-linear theory one can give an answer to the question of how long the initial perturbations can grow and how change the equilibrium state of the plasma current sheet under the reverse effect of these perturbations. We derive a system of nonlinear kinetic equation with self-consistent electromagnetic field in order to study the evolution of the distribution function of the background plasma current sheet in the approximation of low-frequency eigenmodes of instabilities. Evolution equation was obtained for the perturbation of the electromagnetic field and the instability growth rate in the current sheet. Algorithms were tested for solutions of the equations obtained. 1. Lyahov V.V., Neshchadim V.M. Kinetic theory of the current sheath. I. On polarization of an equilibrium current sheath// Advances in Space Research. -2012. -Vol. 50. -P. 318-326. 2. Lyahov V.V., Neshchadim V.M. Kinetic theory of the current sheath. II. Effect of polarization on the stability of a current sheath.// Advances in Space Research.-2013. -Vol. 51. -P. 730-741. 3. Lyahov V.V., Neshchadim V.M. The Effect of Polarization on the Stability of Current Sheaths in Space Plasma // EGU General Assembly 2013, held 7-12 April, 2013 in Vienna, Austria, id. EGU2013-1379, 04/2013, Bibliographic Code: 2013EGUGA..15.1379L 4. Lyahov V.V., Neshchadim V.M. About the eguilibrium and stability of nonelectroneutral current sheats // Advances in Space Research.-2014. -Vol. 54. -P. 901-907.
Institute of Scientific and Technical Information of China (English)
郑神州; 卢寒芳
2012-01-01
In this paper, the analytic properties is considered for a class of subelliptic quasi-linear equations in unbounded exterior domian. we establish various Liuoville theorems in unbounded exterior domain under the different settings with n ≥ 3.%研究一类次椭圆拟线性方程在具有Carnot-Caratheodory空间度量下的外区域的分析性质,得到了在各种情况下无界外区域上的Liouville型定理结论.
Institute of Scientific and Technical Information of China (English)
Yong Fu YANG
2011-01-01
For an inhomogeneous quasilinear hyperbolic system of diagonal form, under the assumptions that the system is linearly degenerate and the C1 norm of the boundary data is bounded, we show that the mechanism of the formation of singularities of C1 classical solution to the Goursat problem with C1 compatibility conditions at the origin must be an ODE type. The similar result is also obtained for the weakly discontinuous solution with C0 compatibility conditions at the origin.
Bradley, William; Bird, Ross; Eldred, Dennis; Zook, Jon; Knowles, Gareth
2013-01-01
This work involved developing spacequalifiable switch mode DC/DC power supplies that improve performance with fewer components, and result in elimination of digital components and reduction in magnetics. This design is for missions where systems may be operating under extreme conditions, especially at elevated temperature levels from 200 to 300 degC. Prior art for radiation-tolerant DC/DC converters has been accomplished utilizing classical magnetic-based switch mode converter topologies; however, this requires specific shielding and component de-rating to meet the high-reliability specifications. It requires complex measurement and feedback components, and will not enable automatic re-optimization for larger changes in voltage supply or electrical loading condition. The innovation is a switch mode DC/DC power supply that eliminates the need for processors and most magnetics. It can provide a well-regulated voltage supply with a gain of 1:100 step-up to 8:1 step down, tolerating an up to 30% fluctuation of the voltage supply parameters. The circuit incorporates a ceramic core transformer in a manner that enables it to provide a well-regulated voltage output without use of any processor components or magnetic transformers. The circuit adjusts its internal parameters to re-optimize its performance for changes in supply voltage, environmental conditions, or electrical loading at the output
Institute of Scientific and Technical Information of China (English)
邹本腾
2001-01-01
本文给出了拟线性抛物型方程Cu=ut-aij(x,t,u)Diju+a(x,t,u,Du)=0在正则斜微商边界条件Bu=biDiu=g下的强解u∈Wq2,1(QT)(q＞n+1)的存在、唯一性.这里我们假设系数aij是Caratheodory函数,且关于(x,t),aij∈VMO ∩L∞;而函数a(x,t,u,Du)关于Du至多是二次增长.
一类拟线性椭圆方程的多重解%Multiplicity Solutions for the Eigenvalue Problem of a Quasilinear Elliptic Equation
Institute of Scientific and Technical Information of China (English)
章国庆; 刘三阳; 冯爱萍
2005-01-01
利用变分法和一个三临界点定理,证明了一类拟线性椭圆方程-div(a|△u|p)| △u| p-2△u)=λf(x,u),Ω,{u=0, aΩ在某些新的条件下至少存在三个解,其中Ω ( )Rn(n≥1)是一个具有光滑边界的有界区域,且a∈C(R+,R),p＞n,λ＞0为一实参数.并给出了该结论在毛细现象中的广义Capillarity方程的一个应用.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Xu, Xiaofeng; Jiao, W H; Zhou, N; Guo, Y; Li, Y K; Dai, Jianhui; Lin, Z Q; Liu, Y J; Zhu, Zengwei; Lu, Xin; Yuan, H Q; Cao, Guanghan
2015-08-26
We report on the quasi-linear in field intrachain magnetoresistance in the normal state of a quasi-one-dimensional superconductor Ta4Pd3Te16 (Tc ~ 4.6 K). Both the longitudinal and transverse in-chain magnetoresistance shows a power-law dependence, Δρ∝B(α) with the exponent α close to 1 over a wide temperature and field range. The magnetoresistance shows no sign of saturation up to 50 T studied. The linear magnetoresistance observed in Ta4Pd3Te16 is found to be overall inconsistent with the interpretations based on the Dirac fermions in the quantum limit, charge conductivity fluctuations as well as quantum electron-electron interference. Moreover, it is observed that the Kohler's rule, regardless of the field orientations, is violated in its normal state. This result suggests the loss of charge carriers in the normal state of this chain-containing compound, due presumably to the charge-density-wave fluctuations.
Kinsella, John J.
1970-01-01
Discussed are the nature of a mathematical problem, problem solving in the traditional and modern mathematics programs, problem solving and psychology, research related to problem solving, and teaching problem solving in algebra and geometry. (CT)
Directory of Open Access Journals (Sweden)
Guo Chun Wen
2009-05-01
Full Text Available This article concerns the oblique derivative problems for second-order quasilinear degenerate equations of mixed type with several characteristic boundaries, which include the Tricomi problem as a special case. First we formulate the problem and obtain estimates of its solutions, then we show the existence of solutions by the successive iterations and the Leray-Schauder theorem. We use a complex analytic method: elliptic complex functions are used in the elliptic domain, and hyperbolic complex functions in the hyperbolic domain, such that second-order equations of mixed type with degenerate curve are reduced to the first order mixed complex equations with singular coefficients. An application of the complex analytic method, solves (1.1 below with $m=n=1$, $a=b=0$, which was posed as an open problem by Rassias.
Winkler, Michael
2017-02-01
The Neumann initial-boundary value problem for the chemotaxis system {ut=∇ṡ(D(u)∇u)-∇ṡ(S(u)∇v),vt=Δv-v+u,(⋆) is considered in a bounded domain Ω \\subset {{{R}}n} , n≥slant 1 , with smooth boundary. In compliance with refined modeling approaches, the diffusivity function D therein is allowed to decay considerably fast at large densities, where a particular focus will be on the mathematically delicate case when D(s) decays exponentially as s\\to ∞ . In such situations, namely, straightforward Moser-type recursive arguments for the derivation of {{L}∞} estimates for u from corresponding L p bounds seem to fail. Accordingly, results on global existence, and especially on quantitative upper bounds for solutions, so far mainly concentrate on cases when D decays at most algebraically, and hence are unavailable in the present context. This work develops an alternative approach, at its core based on a Moser-type iteration for the quantity {{\\text{e}}u} , to establish global existence of classical solutions for all reasonably regular initial data, as well as a logarithmic upper estimate for the possible growth of \\parallel u(\\centerdot,t){{\\parallel}{{L∞}(Ω )}} as t\\to ∞ , under the assumptions that with some K 1 > 0, K 2 > 0, {β-}>0 and {β+}\\in ≤ft(-∞,{β-}\\right] we have {{K}1}{{\\text{e}}-{β-}s}}≤slant D(s)≤slant {{K}2}{{\\text{e}}-{{β+}s}} for all s≥slant 0 , and that the size of S relative to D can be estimated according to \\frac{S(s)}{D(s)}≤slant {{K}3}{{\\text{e}}γ s} for all s≥slant 0 with some K 3 > 0 and γ \\in ≤ft[\\frac{{{β+}-{β-}}{2},\\frac{{β+}}{2}\\right) . Making use of the fact that this allows for certain superalgebraic growth of \\frac{S}{D} , as a particular consequence of this and known results on nonexistence of global bounded solutions we shall see that in the prototypical case when D(s)={{\\text{e}}-β s} and S(s)=s{{\\text{e}}-α s} for all s≥slant 0 and some
Interactions between discontinuities for binary mixture separation problem and hodograph method
Elaeva, M S; Yu, Zhukov M
2016-01-01
The Cauchy problem for first-order PDE with the initial data which have a piecewise discontinuities localized in different spatial points is completely solved. The interactions between discontinuities arising after breakup of initial discontinuities are studied with the help of the hodograph method. The solution is constructed in analytical implicit form. To recovery the explicit form of solution we propose the transformation of the PDEs into some ODEs on the level lines (isochrones) of implicit solution. In particular, this method allows us to solve the Goursat problem with initial data on characteristics. The paper describes a specific problem for zone electrophoresis (method of the mixture separation). However, the method proposed allows to solve any system of two first-order quasilinear PDEs for which the second order linear PDE, arising after the hodograph transformation, has the Riemann-Green function in explicit form.
Tugchin, B. N.; Janunts, N.; Steinert, M.; Dietrich, K.; Kley, E. B.; Tünnermann, A.; Pertsch, T.
2017-06-01
In this study, we investigate analytically and experimentally the roles of quasi-linearly polarized (LP), hybrid, plasmonic and photonic modes in optical detection and excitation with aperture tips in scanning near-field optical microscopy. Aperture tips are tapered and metal-coated optical fibers where small circular apertures are made at the apex. In aperture tips, there exist plasmonic modes that are bound at the interface of the metal cladding to the inner dielectric fiber and photonic modes that are guided in the area of the increased index in the dielectric fiber core. The fundamental photonic mode, although excited by the free-space Gaussian beam, experiences cutoff and turns into an evanescent mode. The photonic mode also becomes lossier than the plasmonic mode toward the tip aperture, and its power decay due to absorption and reflection is expected to be at least 10-9. In contrast, the fundamental plasmonic mode has no cutoff and thus reaches all the way to the tip aperture. Due to the non-adiabaticity of both modes’ propagations through the taper below a core radius of 600 nm, there occurs coupling between the modes. The transmission efficiency of the plasmonic mode, including the coupling efficiency and the propagation loss, is expected to be about 10-6 that is at least 3 orders of magnitude larger than that of the photonic mode. Toward the tip aperture, the longitudinal field of the photonic mode becomes stronger than the transverse ones while the transverse fields always dominate for the plasmonic mode. Experimentally, we obtain polarization resolved images of the near-field at the tip aperture and compare with the x- and y-components of the fundamental quasi-LP plasmonic and photonic modes. The results show that not only the pattern but also the intensity ratios of the x- and y-components of the aperture near-field match with that of the fundamental plasmonic mode. Consequently, we conclude that only the plasmonic mode reaches the tip aperture and
... you are having balance problems, see your doctor. Balance disorders can be signs of other health problems, such ... cases, treating the illness that is causing the disorder will help with the balance problem. Exercises, a change in diet, and some ...
Directory of Open Access Journals (Sweden)
Muhammad Aslam Noor
2004-01-01
Full Text Available We consider a new class of equilibrium problems, known as hemiequilibrium problems. Using the auxiliary principle technique, we suggest and analyze a class of iterative algorithms for solving hemiequilibrium problems, the convergence of which requires either pseudomonotonicity or partially relaxed strong monotonicity. As a special case, we obtain a new method for hemivariational inequalities. Since hemiequilibrium problems include hemivariational inequalities and equilibrium problems as special cases, the results proved in this paper still hold for these problems.
An Inhomogeneous Quasilinear Hyperbolic System.
1980-11-01
bounded variation and v0(x) has a positive bound, Lemma 2.1 • 1 and h < that 1 +a V r(.,t) + V s(.,t) < Q for t < T (2.7) +G +W K2M 24K1T K2 where Q...that u 0(x) are bounded functions with bounded variation , v 0(x) has a positive lower bound. U(u,v,x,t), V(u,v,x,t) are smooth functions satisfying...t) to denote the weak solution of (0.1) and (0.2). Theorem 4.1. Suppose that u0 (x), v0 (x) are bounded functions with bounded variation and do not
Quasi-linear Dialectica Extraction
Trifonov, Trifon
Gödel's functional interpretation [1] can be used to extract programs from non-constructive proofs. Though correct by construction, the obtained terms can be computationally inefficient. One reason for slow execution is the re-evaluation of equal subterms due to the use of substitution during the extraction process. In the present paper we define a variant of the interpretation, which avoids subterm repetition and achieves an almost linear bound on the size of extracted programs.
On strongly degenerate convection-diffusion Problems Modeling sedimentation-consolidation Processes
Energy Technology Data Exchange (ETDEWEB)
Buerger, R.; Evje, S.; Karlsen, S. Hvistendahl
1999-10-01
This report investigates initial-boundary value problems for a quasilinear strongly degenerate convection-diffusion equation with a discontinuous diffusion coefficient. These problems come from the mathematical modelling of certain sedimentation-consolidation processes. Existence of entropy solutions belonging to BV is shown by the vanishing viscosity method. The existence proof for one of the models includes a new regularity result for the integrated diffusion coefficient. New uniqueness proofs for entropy solutions are also presented. These proofs rely on a recent extension to second order equations of Kruzkov`s method of `doubling of the variables`. The application to a sedimentation-consolidation model is illustrated by two numerical examples. 25 refs., 2 figs.
Institute of Scientific and Technical Information of China (English)
张慧; 张福保
2013-01-01
For a class of asymptotically periodic quasilinear Schrödinger equations with critical growth the existence of ground states is proved.First applying a change of variables the quasilinear Schrödinger equations are reduced to semilinear Schrödinger equations in which the corresponding functional is well defined in H1 RN .Moreover there is a one-to-one correspondence between ground states of the semilinear Schrödinger equations and the quasilinear Schrödinger equations.Then the mountain-pass theorem is used to find nontrivial solutions for the semilinear Schrödinger equations. Finally under certain monotonicity conditions using the Nehari manifold method and the concentration compactness principle the nontrivial solutions are found to be exactly the same as the ground states of the semilinear Schrödinger equations.%针对一类具有临界增长的渐进周期的拟线性Schrödinger方程，证明了基态解的存在性。首先利用一个变量代换，将拟线性Schrödinger 方程转化为半线性Schrödinger 方程。半线性Schrödinger 方程的泛函在H1（RN）中定义良好，并且半线性Schrödinger方程和拟线性Schrödinger方程的基态解是一一对应的。然后利用山路引理证明了半线性Schrödinger方程的非平凡解的存在性。最后，在适当的单调性条件下，运用Ne-hari 流形的方法和集中紧性引理证明了得到的非平凡解恰好是半线性Schrödinger方程的基态解。
... de los dientes Video: Getting an X-ray Learning Problems KidsHealth > For Kids > Learning Problems Print A ... for how to make it better. What Are Learning Disabilities? Learning disabilities aren't contagious, but they ...
... your legs or feet Movement disorders such as Parkinson's disease Diseases such as arthritis or multiple sclerosis Vision or balance problems Treatment of walking problems depends on the cause. Physical therapy, surgery, or mobility aids may help.
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Christensen, Anders Bøggild; Rasmussen, Tove; Bundesen, Peter Verner
Sociale problemer kan betragtes som selve udgangspunktet for socialt arbejde, hvor ambitionen er at råde bod på problemerne og sikre, at udsatte borgere får en bedre tilværelse. Det betyder også, at diskussionen af sociale problemer er afgørende for den sociale grundfaglighed. I denne bog sætter en...... række fagfolk på tværs af det danske socialfaglige felt fokus på sociale problemer. Det diskuteres, hvad vi overhovedet forstår ved sociale problemer, hvordan de opstår, hvilke konsekvenser de har, og ikke mindst hvordan man som fagprofessionel håndterer sociale problemer i det daglige arbejde. Bogen er...... skrevet som lærebog til professionsuddannelser, hvor sociale problemer udgør en dimension, bl.a. socialrådgiver-, pædagog- og sygeplejerskeuddannelserne....
Directory of Open Access Journals (Sweden)
Terent'eva Elena Olegovna
2013-09-01
Full Text Available Inner and outer Lamb problems are of extreme importance for various applications in geophysics, as these problems are often used for simulation of wave fields accompanying earthquakes. Solutions of the outer Lamb problem of concentrated force impact applied to the free surface of an elastic half-plane are analyzed in this article. Two solutions are compared: the analytical solution obtained in 1984 and the solution obtained in a modern FEM complex Abaqus.
Terent'eva Elena Olegovna
2013-01-01
Inner and outer Lamb problems are of extreme importance for various applications in geophysics, as these problems are often used for simulation of wave fields accompanying earthquakes. Solutions of the outer Lamb problem of concentrated force impact applied to the free surface of an elastic half-plane are analyzed in this article. Two solutions are compared: the analytical solution obtained in 1984 and the solution obtained in a modern FEM complex Abaqus.
... BMI Calculator myhealthfinder Immunization Schedules Nutrient Shortfall Questionnaire Knee ProblemsPain, swelling, stiffness and "water" on the knee are common symptoms. Follow this chart for more ...
Skovhus, Randi Boelskifte; Thomsen, Rie
2017-01-01
This article introduces a method to critical reviews and explores the ways in which problems have been formulated in knowledge production on career guidance in Denmark over a 10-year period from 2004 to 2014. The method draws upon the work of Bacchi focussing on the "What's the problem represented to be" (WPR) approach. Forty-nine…
Skovhus, Randi Boelskifte; Thomsen, Rie
2017-01-01
This article introduces a method to critical reviews and explores the ways in which problems have been formulated in knowledge production on career guidance in Denmark over a 10-year period from 2004 to 2014. The method draws upon the work of Bacchi focussing on the "What's the problem represented to be" (WPR) approach. Forty-nine…
Reflected forward-backward SDEs and obstacle problems with boundary conditions
Directory of Open Access Journals (Sweden)
Jin Ma
2001-01-01
Full Text Available In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short. More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.
... do to help diagnose your prostate problem. Physical Exam A physical exam may help diagnose the cause ... sleep avoid or drink fewer liquids that have caffeine or alcohol in them avoid medicines that may ...
DEFF Research Database (Denmark)
Skovhus, Randi Boelskifte; Thomsen, Rie
2016-01-01
This article introduces a method to critical reviews and explores the ways in which problems have been formulated in knowledge production on career guidance in Denmark over a 10-year period from 2004 to 2014. The method draws upon the work of Bacchi focussing on the ‘What's the problem represented...... to be’ (WPR) approach. Forty-nine empirical studies on Danish youth career guidance were included in the study. An analysis of the issues in focus resulted in nine problem categories. One of these, ‘targeting’, is analysed using the WPR approach. Finally, the article concludes that the WPR approach...... provides a constructive basis for a critical analysis and discussion of the collective empirical knowledge production on career guidance, stimulating awareness of problems and potential solutions among the career guidance community....
... our e-newsletter! Aging & Health A to Z Kidney Problems Basic Facts & Information The kidneys are two ... the production of red blood cells. What are Kidney Diseases? For about one-third of older people, ...
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... Ear Nose & Throat Emotional Problems Eyes Fever From Insects or Animals Genitals and Urinary Tract Glands & Growth ... an irregular shape (astigmatism), it will threaten normal vision development and must be corrected as early as ...
Kellerer, Hans; Pisinger, David
2004-01-01
Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back in 1990: "How can you write 250 pages on the knapsack problem?" Indeed, the definition of the knapsack problem is easily understood even by a non-expert who will not suspect the presence of challenging research topics in this area at the first glance. However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes. Moreover, the extension of the knapsack problem to higher dimensions both in the number of constraints and in the num ber of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years. Hence, two years ago ...
Baronti, Marco; van der Putten, Robertus; Venturi, Irene
2016-01-01
This book, intended as a practical working guide for students in Engineering, Mathematics, Physics, or any other field where rigorous calculus is needed, includes 450 exercises. Each chapter starts with a summary of the main definitions and results, which is followed by a selection of solved exercises accompanied by brief, illustrative comments. A selection of problems with indicated solutions rounds out each chapter. A final chapter explores problems that are not designed with a single issue in mind but instead call for the combination of a variety of techniques, rounding out the book’s coverage. Though the book’s primary focus is on functions of one real variable, basic ordinary differential equations (separation of variables, linear first order and constant coefficients ODEs) are also discussed. The material is taken from actual written tests that have been delivered at the Engineering School of the University of Genoa. Literally thousands of students have worked on these problems, ensuring their real-...
... have cold or flu symptoms?YesNoDo you have tooth pain on the same side as the ear pain ... or 2 days, see your doctor.Start OverDiagnosisA tooth problem can radiate pain to the ear on the same side.Self ...
1987-06-01
and f. Let us consider the problem of finding the minimal constant C. We are thus interested in 2~ IVA u dx (1.24) C = sup . u2u (0 (F =0 (u dx"<u(O...fournir des bornes superieures ou inferieures, C.R. Acad. Sci., Paris 235, 995-997. .V Prodi, G. (1962]: Theoremi di tipo locale per il sistema de Navier
Directory of Open Access Journals (Sweden)
Yaping Hu
2015-01-01
the nonsmooth convex optimization problem. First, by using Moreau-Yosida regularization, we convert the original objective function to a continuously differentiable function; then we use approximate function and gradient values of the Moreau-Yosida regularization to substitute the corresponding exact values in the algorithm. The global convergence is proved under suitable assumptions. Numerical experiments are presented to show the effectiveness of this algorithm.
Asymptotics of the filtration problem for suspension in porous media
Directory of Open Access Journals (Sweden)
Kuzmina Ludmila Ivanovna
2015-01-01
Full Text Available The mechanical-geometric model of the suspension filtering in the porous media is considered. Suspended solid particles of the same size move with suspension flow through the porous media - a solid body with pores - channels of constant cross section. It is assumed that the particles pass freely through the pores of large diameter and are stuck at the inlet of pores that are smaller than the particle size. It is considered that one particle can clog only one small pore and vice versa. The particles stuck in the pores remain motionless and form a deposit. The concentrations of suspended and retained particles satisfy a quasilinear hyperbolic system of partial differential equations of the first order, obtained as a result of macro-averaging of micro-stochastic diffusion equations. Initially the porous media contains no particles and both concentrations are equal to zero; the suspension supplied to the porous media inlet has a constant concentration of suspended particles. The flow of particles moves in the porous media with a constant speed, before the wave front the concentrations of suspended and retained particles are zero. Assuming that the filtration coefficient is small we construct an asymptotic solution of the filtration problem over the concentration front. The terms of the asymptotic expansions satisfy linear partial differential equations of the first order and are determined successively in an explicit form. It is shown that in the simplest case the asymptotics found matches the known asymptotic expansion of the solution near the concentration front.
Inverse modeling for heat conduction problem in human abdominal phantom.
Huang, Ming; Chen, Wenxi
2011-01-01
Noninvasive methods for deep body temperature measurement are based on the principle of heat equilibrium between the thermal sensor and the target location theoretically. However, the measurement position is not able to be definitely determined. In this study, a 2-dimensional mathematical model was built based upon some assumptions for the physiological condition of the human abdomen phantom. We evaluated the feasibility in estimating the internal organs temperature distribution from the readings of the temperature sensors arranged on the skin surface. It is a typical inverse heat conduction problem (IHCP), and is usually mathematically ill-posed. In this study, by integrating some physical and physiological a-priori information, we invoked the quasi-linear (QL) method to reconstruct the internal temperature distribution. The solutions of this method were improved by increasing the accuracy of the sensors and adjusting their arrangement on the outer surface, and eventually reached the state of converging at the best state accurately. This study suggests that QL method is able to reconstruct the internal temperature distribution in this phantom and might be worthy of a further study in an anatomical based model.
Oleschko, K.; Khrennikov, A. Yu.
2017-01-01
In a very general setting, we discuss possibilities of applying p-adics to geophysics using a p-adic diffusion representation of the master equations for the dynamics of a fluid in capillaries in porous media and formulate several mathematical problems motivated by such applications. We stress that p-adic wavelets are a powerful tool for obtaining analytic solutions of diffusion equations. Because p-adic diffusion is a special case of fractional diffusion, which is closely related to the fractal structure of the configuration space, p-adic geophysics can be regarded as a new approach to fractal modeling of geophysical processes.
Directory of Open Access Journals (Sweden)
Xin-He Miao
2012-01-01
Full Text Available This paper investigates the Lipschitz continuity of the solution mapping of symmetric cone (linear or nonlinear complementarity problems (SCLCP or SCCP, resp. over Euclidean Jordan algebras. We show that if the transformation has uniform Cartesian P-property, then the solution mapping of the SCCP is Lipschitz continuous. Moreover, we establish that the monotonicity of mapping and the Lipschitz continuity of solutions of the SCLCP imply ultra P-property, which is a concept recently developed for linear transformations on Euclidean Jordan algebra. For a Lyapunov transformation, we prove that the strong monotonicity property, the ultra P-property, the Cartesian P-property, and the Lipschitz continuity of the solutions are all equivalent to each other.
Many men have sexual problems. They become more common as men age. Problems can include Erectile dysfunction Reduced or lost interest in sex ... problems may also be factors. Occasional problems with sexual function are common. If problems last more than ...
Das, Animesh; Gieb, Klaus; Krupskaya, Yulia; Demeshko, Serhiy; Dechert, Sebastian; Klingeler, Rüdiger; Kataev, Vladislav; Büchner, Bernd; Müller, Paul; Meyer, Franc
2011-03-16
First members of a new family of heterometallic Mn/Ni complexes [Mn(2)Ni(3)X(2)L(4)(LH)(2)(H(2)O)(2)] (X = Cl: 1; X = Br: 2) with the new ligand 2-{3-(2-hydroxyphenyl)-1H-pyrazol-1-yl}ethanol (H(2)L) have been synthesized, and single crystals obtained from CH(2)Cl(2) solutions have been characterized crystallographically. The molecular structures feature a quasi-linear Mn(III)-Ni(II)-Ni(II)-Ni(II)-Mn(III) core with six-coordinate metal ions, where elongated axes of all the distorted octahedral coordination polyhedra are aligned parallel and are fixed with respect to each other by intramolecular hydrogen bonds. 1 and 2 exhibit quite strong ferromagnetic exchange interactions throughout (J(Mn-Ni) ≈ 40 K (1) or 42 K (2); J(Ni-Ni) ≈ 22 K (1) or 18 K (2)) that lead to an S(tot) = 7 ground state, and a sizable uniaxial magnetoanisotropy with D(mol) values -0.55 K (1) and -0.45 K (2). These values are directly derived also from frequency- and temperature-dependent high-field EPR spectra. Slow relaxation of the magnetization at low temperatures and single-molecule magnet (SMM) behavior are evident from frequency-dependent peaks in the out-of-phase ac susceptibilities and magnetization versus dc field measurements, with significant energy barriers to spin reversal U(eff) = 27 K (1) and 22 K (2). Pronounced quantum tunnelling steps are observed in the hysteresis loops of the temperature- and scan rate-dependent magnetization data, but with the first relaxation step shifted above (1) or below (2) the zero crossing of the magnetic field, despite the very similar molecular structures. The different behavior of 1 and 2 is interpreted in terms of antiferromagnetic (1) or ferromagnetic (2) intermolecular interactions, which are discussed in view of the subtle differences of intermolecular contacts within the crystal lattice.
... Other Dental Problems Diabetes & Sexual & Urologic Problems Preventing Diabetes Problems View or Print All Sections Heart Disease & ... prevent or delay sexual and urologic problems. Depression & Diabetes Depression is common among people with a chronic, ...
A quasilinear formulation of turbulence driven current
Energy Technology Data Exchange (ETDEWEB)
McDevitt, C. J.; Tang, Xian-Zhu; Guo, Zehua [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2014-02-15
Non-inductive current drive mechanisms, such as the familiar neoclassical bootstrap current correspond to an essential component to the realization of steady state tokamak operation. In this work, we discuss a novel collisionless mechanism through which a mean plasma current may be driven in the presence of microturbulence. In analogy with the traditional neoclassical bootstrap current drive mechanism, in which the collisional equilibrium established between trapped and passing electrons results in the formation of a steady state plasma current, here we show that resonant scattering of electrons by drift wave microturbulence provides an additional means of determining the equilibrium between trapped and passing electrons. The resulting collisionless equilibrium is shown to result in the formation of an equilibrium current whose magnitude is a function of the thermodynamic forces. A mean field formulation is utilized to incorporate the above components into a unified framework through which both collisional as well as collisionless current drive mechanisms may be self-consistently treated. Utilizing a linearized Fokker-Planck collision operator, the plasma current in the presence of both collisions as well as turbulent stresses is computed, allowing for the relative strength of these two mechanisms to be quantified as a function of collisionality and fluctuation amplitude.
On some quasilinear structured population models
Getto, P.
2005-01-01
The object of my research was the mathematical analysis of a class of population models in which the effect of differences of individuals (in e.g. age, size or position in space) on their physiological development, mortality and reproduction is assumed to play an important role. Such models, which a
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
Class and Home Problems: Optimization Problems
Anderson, Brian J.; Hissam, Robin S.; Shaeiwitz, Joseph A.; Turton, Richard
2011-01-01
Optimization problems suitable for all levels of chemical engineering students are available. These problems do not require advanced mathematical techniques, since they can be solved using typical software used by students and practitioners. The method used to solve these problems forces students to understand the trends for the different terms…
Reeves, Charles A.
2000-01-01
Uses the chicken problem for sixth grade students to scratch the surface of systems of equations using intuitive approaches. Provides students responses to the problem and suggests similar problems for extensions. (ASK)
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Constipation and Defecation Problems
... Home / Digestive Health Topic / Constipation and Defecation Problems Constipation and Defecation Problems Basics Resources Overview Constipation is one of the most frequent gastrointestinal complaints ...
Kent, James; Holdaway, Daniel
2015-01-01
A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.
Institute of Scientific and Technical Information of China (English)
Li WANG; Jixiu WANG
2014-01-01
Let B1 ⊂ RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients:-div(|∇u|p-2∇u)=|x|s|u|p*(s)-2u+λ|x|t|u|p-2u, x∈B1, u|∂B1 =0, where t, s>-p, 2≤pp(p-1)t+p(p2-p+1) andλ∈(0,λ1,t), whereλ1,t is the first eigenvalue of-∆p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ (ps+p) min{1, p+tp+s}+p2p-(p-1) min{1, p+tp+s} andλ>0 is small.
WALLS, FOREST
PRESENT MIGRANT LABOR PROBLEMS AND SOLUTIONS WHICH HAVE BEEN PROPOSED ARE PRESENTED. THE FIRST PROBLEM AREA IS PROVIDING EDUCATION FOR MIGRANT CHILDREN. THIS IS HINDERED BY THE PROBLEM OF SECURING COMPLIANCE WITH MINIMUM EDUCATION LAWS AND BY LAWS PROHIBITING EMPLOYMENT OF CHILDREN DURING SCHOOL HOURS. A SECOND PROBLEM AREA IS THAT OF CHILD LABOR.…
Cheryl A. Smith
2008-01-01
Diagnosing Christmas tree problems can be a challenge, requiring a basic knowledge of plant culture and physiology, the effect of environmental influences on plant health, and the ability to identify the possible causes of plant problems. Developing a solution or remedy to the problem depends on a proper diagnosis, a process that requires recognition of a problem and...
Quadratic eigenvalue problems.
Energy Technology Data Exchange (ETDEWEB)
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
Problem solving III: factors influencing classroom problem
Directory of Open Access Journals (Sweden)
Sayonara Salvador Cabral da Costa
1997-05-01
Full Text Available This paper presents a review of the literature in the area of problem solving, particularly in physics, focusing only on factors that influence classroom problem solving. Fifty-seven papers have been analyzed in terms of theoretical basis, investigated factors/methodology and findings/relevant factors, which were organized in a table that served as support for a synthesis made by the authors. It is the third of a four-paper series reviewing different aspects of the problem solving subject.
HT2DINV: A 2D forward and inverse code for steady-state and transient hydraulic tomography problems
Soueid Ahmed, A.; Jardani, A.; Revil, A.; Dupont, J. P.
2015-12-01
Hydraulic tomography is a technique used to characterize the spatial heterogeneities of storativity and transmissivity fields. The responses of an aquifer to a source of hydraulic stimulations are used to recover the features of the estimated fields using inverse techniques. We developed a 2D free source Matlab package for performing hydraulic tomography analysis in steady state and transient regimes. The package uses the finite elements method to solve the ground water flow equation for simple or complex geometries accounting for the anisotropy of the material properties. The inverse problem is based on implementing the geostatistical quasi-linear approach of Kitanidis combined with the adjoint-state method to compute the required sensitivity matrices. For undetermined inverse problems, the adjoint-state method provides a faster and more accurate approach for the evaluation of sensitivity matrices compared with the finite differences method. Our methodology is organized in a way that permits the end-user to activate parallel computing in order to reduce the computational burden. Three case studies are investigated demonstrating the robustness and efficiency of our approach for inverting hydraulic parameters.
Differential equations problem solver
Arterburn, David R
2012-01-01
REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and
Every pregnancy has some risk of problems. The causes can be conditions you already have or conditions you develop. ... pregnant with more than one baby, previous problem pregnancies, or being over age 35. They can affect ...
... Read MoreDepression in Children and TeensRead MoreBMI Calculator Menstrual Cycle ProblemsFrom missed periods to painful periods, menstrual cycle problems are common, but usually not serious. Follow ...
Challenging problems in algebra
Posamentier, Alfred S
1996-01-01
Over 300 unusual problems, ranging from easy to difficult, involving equations and inequalities, Diophantine equations, number theory, quadratic equations, logarithms, more. Detailed solutions, as well as brief answers, for all problems are provided.
... Ear Nose & Throat Emotional Problems Eyes Fever From Insects or Animals Genitals and Urinary Tract Glands & Growth ... important distinction is that this is not a vision problem ; rather, the brain is reversing, inverting or ...
Problem Solving and Reasoning.
1984-02-01
6 here Acquisition of Problem - Solving Skill . An imporrant qLestinn is how the knowledge required For solving problems in a domain such as geometry is...Neves, 0. 4. (1981). Acquisition of problem - solving skill . In J. R. Anderson (Eds), Cognitive skills and their acquisition. Hillsdale, NJ: Erlbaum...NJ: Erlbaum. Voss, J. F., Greene, T. R., Post, T. A., & Penner, B. C. (1983). Problem solving skill in the social sciences. In G. H. Bower (Ed.), The
Classifying IS Project Problems
DEFF Research Database (Denmark)
Munk-Madsen, Andreas
2006-01-01
The literature contains many lists of IS project problems, often in the form of risk factors. The problems sometimes appear unordered and overlapping, which reduces their usefulness to practitioners as well as theoreticians. This paper proposes a list of criteria for formulating project problems...
Vehicle Routing Problem Models
Directory of Open Access Journals (Sweden)
Tonči Carić
2004-01-01
Full Text Available The Vehicle Routing Problem cannot always be solved exactly,so that in actual application this problem is solved heuristically.The work describes the concept of several concrete VRPmodels with simplified initial conditions (all vehicles are ofequal capacity and start from a single warehouse, suitable tosolve problems in cases with up to 50 users.
Optimal obstacle control problem
Institute of Scientific and Technical Information of China (English)
ZHU Li; LI Xiu-hua; GUO Xing-ming
2008-01-01
In the paper we discuss some properties of the state operators of the optimal obstacle control problem for elliptic variational inequality. Existence, uniqueness and regularity of the optimal control problem are established. In addition, the approximation of the optimal obstacle problem is also studied.
Mathematics as Problem Solving.
Soifer, Alexander
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
Pelleau, Marie; Truchet, Charlotte
2009-01-01
This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP) and the Intra-ring Synchronous Optical Network Design Problem (IDP). These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results.
Baras, John
2010-01-01
The algebraic path problem is a generalization of the shortest path problem in graphs. Various instances of this abstract problem have appeared in the literature, and similar solutions have been independently discovered and rediscovered. The repeated appearance of a problem is evidence of its relevance. This book aims to help current and future researchers add this powerful tool to their arsenal, so that they can easily identify and use it in their own work. Path problems in networks can be conceptually divided into two parts: A distillation of the extensive theory behind the algebraic path pr
Directory of Open Access Journals (Sweden)
Marie Pelleau
2009-10-01
Full Text Available This paper presents a new method and a constraint-based objective function to solve two problems related to the design of optical telecommunication networks, namely the Synchronous Optical Network Ring Assignment Problem (SRAP and the Intra-ring Synchronous Optical Network Design Problem (IDP. These network topology problems can be represented as a graph partitioning with capacity constraints as shown in previous works. We present here a new objective function and a new local search algorithm to solve these problems. Experiments conducted in Comet allow us to compare our method to previous ones and show that we obtain better results.
Energy Technology Data Exchange (ETDEWEB)
Pan, Feng [Los Alamos National Laboratory; Kasiviswanathan, Shiva [Los Alamos National Laboratory
2010-01-01
In the matrix interdiction problem, a real-valued matrix and an integer k is given. The objective is to remove k columns such that the sum over all rows of the maximum entry in each row is minimized. This combinatorial problem is closely related to bipartite network interdiction problem which can be applied to prioritize the border checkpoints in order to minimize the probability that an adversary can successfully cross the border. After introducing the matrix interdiction problem, we will prove the problem is NP-hard, and even NP-hard to approximate with an additive n{gamma} factor for a fixed constant {gamma}. We also present an algorithm for this problem that achieves a factor of (n-k) mUltiplicative approximation ratio.
The Accelerated Kepler Problem
Namouni, Fathi
2007-01-01
The accelerated Kepler problem is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem's Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the accelerated Kepler problem and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.
Rǎdulescu, Teodora-Liliana T.; Andreescu, Titu; Rǎdulescu, Vicenţiu
2015-01-01
This book ontains a collection of challenging problems in elementary mathematical analysis, uses competition-inspired problems as a platform for training typical inventive skills, develops basic valuable techniques for solving problems in mathematical analysis on the real axis, assumes only a basic knowledge of the topic but opens the path to competitive research in the field, includes interesting and valuable historical accounts of ideas and methods in analysis, presents a connection between...
Laughlin, Patrick R
2011-01-01
Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical
Creativity for Problem Solvers
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2009-01-01
This paper presents some modern and interdisciplinary concepts about creativity and creative processes specially related to problem solving. Central publications related to the theme are briefly reviewed. Creative tools and approaches suitable to support problem solving are also presented. Finally......, the paper outlines the author’s experiences using creative tools and approaches to: Facilitation of problem solving processes, strategy development in organisations, design of optimisation systems for large scale and complex logistic systems, and creative design of software optimisation for complex non...
Directory of Open Access Journals (Sweden)
Radovanović Saša Ž.
2014-01-01
Full Text Available The author explains the link between fundamental ontology and metontology in Heidegger's thought. In this context, he raises the question about art as a metontological problem. Then he goes to show that the problem of metontology stems from imanent transformation of fundamental ontology. In this sense, two aspects of the problem of existence assume relevance, namely, universality and radicalism. He draws the conclusion that metontology and art as its problem, as opposed to fundamental ontology, were not integrated into Heidegger's later thought.
Known TCP Implementation Problems
Paxson, Vern (Editor); Allman, Mark; Dawson, Scott; Fenner, William; Griner, Jim; Heavens, Ian; Lahey, K.; Semke, J.; Volz, B.
1999-01-01
This memo catalogs a number of known TCP implementation problems. The goal in doing so is to improve conditions in the existing Internet by enhancing the quality of current TCP/IP implementations. It is hoped that both performance and correctness issues can be resolved by making implementors aware of the problems and their solutions. In the long term, it is hoped that this will provide a reduction in unnecessary traffic on the network, the rate of connection failures due to protocol errors, and load on network servers due to time spent processing both unsuccessful connections and retransmitted data. This will help to ensure the stability of the global Internet. Each problem is defined as follows: Name of Problem The name associated with the problem. In this memo, the name is given as a subsection heading. Classification one or more problem categories for which the problem is classified: "congestion control", "performance", "reliability", "resource management". Description A definition of the problem, succinct but including necessary background material. Significance A brief summary of the sorts of environments for which the problem is significant.
Singh, Devraj
2015-01-01
Numerical Problems in Physics, Volume 1 is intended to serve the need of the students pursuing graduate and post graduate courses in universities with Physics and Materials Science as subject including those appearing in engineering, medical, and civil services entrance examinations. KEY FEATURES: * 29 chapters on Optics, Wave & Oscillations, Electromagnetic Field Theory, Solid State Physics & Modern Physics * 540 solved numerical problems of various universities and ompetitive examinations * 523 multiple choice questions for quick and clear understanding of subject matter * 567 unsolved numerical problems for grasping concepts of the various topic in Physics * 49 Figures for understanding problems and concept
Specific Pronunciation Problems.
Avery, Peter; And Others
1987-01-01
Reviews common pronunciation problems experienced by learners of English as a second language who are native speakers of Vietnamese, Cantonese, Spanish, Portuguese, Italian, Polish, Greek, and Punjabi. (CB)
Energy Technology Data Exchange (ETDEWEB)
Laporte, G.
1987-01-01
Location-routing problems involve simultaneously locating a number of facilities among candidate sites and establishing delivery routes to a set of users in such a way that the total system cost is minimized. This paper presents a survey of such problems. It includes some applications and examples of location-routing problems, a description of the main heuristics that have been developed for such problems, and reviews of various formulations and algorithms used in solving these problems. A more detailed review is given of exact algorithms for the vehicle routing problem, three-index vehicle flow formulations, and two-index vehicle flow formulations and algorithms for symmetrical and non-symmetrical problems. It is concluded that location-routing problem research is a fast-growing area, with most developments occurring over the past few years; however, research is relatively fragmented, often addresses problems which are too specific and contains several voids which have yet to be filled. A number of promising research areas are identified. 137 refs., 3 figs.
Combinatorial problems and exercises
Lovász, László
2007-01-01
The main purpose of this book is to provide help in learning existing techniques in combinatorics. The most effective way of learning such techniques is to solve exercises and problems. This book presents all the material in the form of problems and series of problems (apart from some general comments at the beginning of each chapter). In the second part, a hint is given for each exercise, which contains the main idea necessary for the solution, but allows the reader to practice the techniques by completing the proof. In the third part, a full solution is provided for each problem. This book w
PROBLEMS OF TURKISH LEXICOGRAPHY.
TIETZE, ANDREAS
THE LEXICOGRAPHICAL PROBLEMS IN THE TURKISH LANGUAGE WERE DISCUSSED. HISTORICAL REVIEW OF THE LANGUAGE WAS PRESENTED WITH PROBLEMS OF LEXICOGRAPHY THAT EXISTED IN THE PAST COMPARED WITH THOSE OF THE PRESENT. DISCUSSION TOPICS OF THE REPORT INCLUDED (1) NAME OF THE LANGUAGE, (2) DELIMITATION COMPARED WITH RELATED LANGUAGES, (3) DELIMINATION…
A Stochastic Employment Problem
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Problems in baryon spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Capstick, S. [Florida State Univ., Tallahassee, FL (United States)
1994-04-01
Current issues and problems in the physics of ground- and excited-state baryons are considered, and are classified into those which should be resolved by CEBAF in its present form, and those which may require CEBAF to undergo an energy upgrade to 8 GeV or more. Recent theoretical developments designed to address these problems are outlined.
Problem Solving Techniques Seminar.
Massachusetts Career Development Inst., Springfield.
This booklet is one of six texts from a workplace literacy curriculum designed to assist learners in facing the increased demands of the workplace. Six problem-solving techniques are developed in the booklet to assist individuals and groups in making better decisions: problem identification, data gathering, data analysis, solution analysis,…
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai Juul
2006-01-01
as a general approach to problem solving. We apply these Simonian ideas to organisational issues, specifically new organisational forms. Specifically, Simonian ideas allow us to develop a morphology of new organisational forms and to point to some design problems that characterise these forms....
DEFF Research Database (Denmark)
Ovesen, Nis
2015-01-01
Problem-based learning (PBL) is becoming increasingly popular in design educations, but how is it taught and practiced? This paper presents a case study of a three-day workshop that has the purpose of introducing PBL to design students. A theoretical background on PBL and problems in design is es...
Gladwell, Graham ML
2011-01-01
The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Barrell, Arthur Rex
1970-01-01
The study of semantics, the study of meaning, promises more complete communicative thought transfer if several problem areas can be solved or at least generally agreed upon. The problem of exact definition of words arises from the fact that no one work is the exact equivalent of another. However, the study of many languages forces the mind to…
STONE, EDWARD
THE REPORT POINTS OUT THAT, IN GENERAL, CHRONIC PROBLEM PARENTS GREW UP IN ENVIRONMENTS OF EMOTIONAL IMPOVERISHMENT, INCONSISTENCY, CONFUSION, AND DISORDER, OFTEN WITH DEPRIVATION OF FOOD, CLOTHING, AND SHELTER. THESE PARENTS CATEGORIZE PEOPLE AS THOSE WHO GIVE AND THOSE WHO TAKE. THEY BLAME THEIR PROBLEMS ON EXTERNAL CIRCUMSTANCES NOT UNDER THEIR…
Wicked Problems: Inescapable Wickedity
Jordan, Michelle E.; Kleinsasser, Robert C.; Roe, Mary F.
2014-01-01
The article explores the concept of wicked problems and proposes a reinvigorated application of this concept for wider educational use. This recommendation stems from the contributions of a number of scholars who frame some of the most contentious and recalcitrant educational issues as wicked problems. The present authors build upon these previous…
... hip problems later in life? ResourcesScreening for Developmental Dysplasia of the Hip by LM French, M.D., and FR Dietz, ... 2014 Categories: Family Health, Infants and ToddlersTags: dislocation, dysplasia, external, femoral, hip, infants, internal, problems, socket, torsion Family Health, Infants ...
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Meng, G.; Heragu, S.S.; Zijm, H.
2004-01-01
This paper addresses the reconfigurable layout problem, which differs from traditional, robust and dynamic layout problems mainly in two aspects: first, it assumes that production data are available only for the current and upcoming production period. Second, it considers queuing performance measure
Meng, G.; Heragu, S.S.; Heragu, S.S.; Zijm, Willem H.M.
2004-01-01
This paper addresses the reconfigurable layout problem, which differs from traditional, robust and dynamic layout problems mainly in two aspects: first, it assumes that production data are available only for the current and upcoming production period. Second, it considers queuing performance measure
Current Social Problem Novels.
Kenney, Donald J.
This review of social problem novels for young adults opens with a brief background of the genre, then lists the dominant themes of social problem fiction and nonfiction novels that have been published in the last two years, such as alcoholism, alienation, death, growing up and self-awarness, drugs, and divorce. Other themes mentioned are…
Harper, Kathleen A.; Etkina, Eugenia
2002-10-01
As part of weekly reports,1 structured journals in which students answer three standard questions each week, they respond to the prompt, If I were the instructor, what questions would I ask or problems assign to determine if my students understood the material? An initial analysis of the results shows that some student-generated problems indicate fundamental misunderstandings of basic physical concepts. A further investigation explores the relevance of the problems to the week's material, whether the problems are solvable, and the type of problems (conceptual or calculation-based) written. Also, possible links between various characteristics of the problems and conceptual achievement are being explored. The results of this study spark many more questions for further work. A summary of current findings will be presented, along with its relationship to previous work concerning problem posing.2 1Etkina, E. Weekly Reports;A Two-Way Feedback Tool, Science Education, 84, 594-605 (2000). 2Mestre, J.P., Probing Adults Conceptual Understanding and Transfer of Learning Via Problem Posing, Journal of Applied Developmental Psychology, 23, 9-50 (2002).
Problems in equilibrium theory
Aliprantis, Charalambos D
1996-01-01
In studying General Equilibrium Theory the student must master first the theory and then apply it to solve problems. At the graduate level there is no book devoted exclusively to teaching problem solving. This book teaches for the first time the basic methods of proof and problem solving in General Equilibrium Theory. The problems cover the entire spectrum of difficulty; some are routine, some require a good grasp of the material involved, and some are exceptionally challenging. The book presents complete solutions to two hundred problems. In searching for the basic required techniques, the student will find a wealth of new material incorporated into the solutions. The student is challenged to produce solutions which are different from the ones presented in the book.
Trahtman, A N
2007-01-01
The synchronizing word of deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into deterministic finite automaton possessing a synchronizing word. The road coloring problem is a problem of synchronizing coloring of directed finite strongly connected graph with constant outdegree of all its vertices if the greatest common divisor of lengths of all its cycles is one. The problem was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked a noticeable interest among the specialists in theory of graphs, deterministic automata and symbolic dynamics. The problem is described even in "Vikipedia" - the popular Internet Encyclopedia. The positive solution of the road coloring problem is presented.
The Guderley problem revisited
Energy Technology Data Exchange (ETDEWEB)
Ramsey, Scott D [Los Alamos National Laboratory; Kamm, James R [Los Alamos National Laboratory; Bolstad, John H [NON LANL
2009-01-01
The self-similar converging-diverging shock wave problem introduced by Guderley in 1942 has been the source of numerous investigations since its publication. In this paper, we review the simplifications and group invariance properties that lead to a self-similar formulation of this problem from the compressible flow equations for a polytropic gas. The complete solution to the self-similar problem reduces to two coupled nonlinear eigenvalue problems: the eigenvalue of the first is the so-called similarity exponent for the converging flow, and that of the second is a trajectory multiplier for the diverging regime. We provide a clear exposition concerning the reflected shock configuration. Additionally, we introduce a new approximation for the similarity exponent, which we compare with other estimates and numerically computed values. Lastly, we use the Guderley problem as the basis of a quantitative verification analysis of a cell-centered, finite volume, Eulerian compressible flow algorithm.
Directory of Open Access Journals (Sweden)
Dan Ophir
2011-12-01
Full Text Available The process of making complex and controversial decisions, that is, dealing with moral or ethical dilemmas, have intrigued people and inspired writers from time immemorial. Dilemmas give both color and depth to characters in good literary works. But beyond literary fiction, dilemmas occupy society in every day issues such as in introducing legislation or solving current political problems. One example of a current political dilemma is how to deal with Iran’s quest for nuclear weapons. If it were possible to assess and quantify each of the alternative solutions for a given problem, the process of decision making would be much easier. If a problem involves only two optional solutions, game theory techniques can be used. However, real life problems are usually multi-unit, multi-optional problems, as in Iran
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Boots, Byron
2011-01-01
Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together and allowing information to flow between them, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias in the same way that an instrumental variable allows us to remove bias in a {linear} dimensionality reduction problem. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space. Finally, we discuss situations where two-manifold problems are useful, and demonstrate that sol...
Dürr, Christoph; Spieksma, Frits C R; Nobibon, Fabrice Talla; Woeginger, Gerhard J
2011-01-01
For a given set of intervals on the real line, we consider the problem of ordering the intervals with the goal of minimizing an objective function that depends on the exposed interval pieces (that is, the pieces that are not covered by earlier intervals in the ordering). This problem is motivated by an application in molecular biology that concerns the determination of the structure of the backbone of a protein. We present polynomial-time algorithms for several natural special cases of the problem that cover the situation where the interval boundaries are agreeably ordered and the situation where the interval set is laminar. Also the bottleneck variant of the problem is shown to be solvable in polynomial time. Finally we prove that the general problem is NP-hard, and that the existence of a constant-factor-approximation algorithm is unlikely.
Structural Identification Problem
Directory of Open Access Journals (Sweden)
Suvorov Aleksei
2016-01-01
Full Text Available The identification problem of the existing structures though the Quasi-Newton and its modification, Trust region algorithms is discussed. For the structural problems, which could be represented by means of the mathematical modelling of the finite element code discussed method is extremely useful. The nonlinear minimization problem of the L2 norm for the structures with linear elastic behaviour is solved by using of the Optimization Toolbox of Matlab. The direct and inverse procedures for the composition of the desired function to minimize are illustrated for the spatial 3D truss structure as well as for the problem of plane finite elements. The truss identification problem is solved with 2 and 3 unknown parameters in order to compare the computational efforts and for the graphical purposes. The particular commands of the Matlab codes are present in this paper.
The Interaction Programming Problem
Institute of Scientific and Technical Information of China (English)
LI Rong-sheng; CHENG Ying
2001-01-01
Based upon the research to the economic equilibrium problems, we present a kind of new mathematical programming problem-interaction programming problem (abbreviated by IPP). The IPP is composed of two or multiple parametric programming problems which is interrelated with each other. The IPP reflects the equality and mutual benefit relationship between two (or among multiple) economic planners in an economic system. In essence, the IPP is similar to the generalized Nash equilibria (GNE) game which has been given several names in the literature: social equilibria games, pseudo-Nash equilibria games, and equilibrium programming problems. In this paper, we establish the mathematical model and some basic concepts to the IPP. We investigate the structure and the properties of the IPP. We also give a necessary and sufficient conditions for the existence of the equilibrium points to a kind of linear IPP.
Singh, Chandralekha
2016-01-01
One finding of cognitive research is that people do not automatically acquire usable knowledge by spending lots of time on task. Because students' knowledge hierarchy is more fragmented, "knowledge chunks" are smaller than those of experts. The limited capacity of short term memory makes the cognitive load high during problem solving tasks, leaving few cognitive resources available for metacognition. The abstract nature of the laws of physics and the chain of reasoning required to draw meaningful inferences makes these issues critical. In order to help students, it is crucial to consider the difficulty of a problem from the perspective of students. We are developing and evaluating interactive problem-solving tutorials to help students in the introductory physics courses learn effective problem-solving strategies while solidifying physics concepts. The self-paced tutorials can provide guidance and support for a variety of problem solving techniques, and opportunity for knowledge and skill acquisition.
Problems of energy supply. Probleme der Energieversorgung
Energy Technology Data Exchange (ETDEWEB)
Frank, W.
1983-01-01
Political education is to enable judgement of present-day questions. This requires knowledge of the essential facts in the field of energy supply. The brochure on hand is meant to make it easier for the reader to put forward his own arguments. The reader is to see that it is due to the many motives determining energy policy which aggravate an understanding about ways of solving problems of energy supply. This brochure is designed to enhance political education by giving a survey of tasks in energy policy to be solved on an international level and in Austria.
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations.
Cumulative Vehicle Routing Problems
Kara, &#;mdat; Kara, Bahar Yeti&#;; Yeti&#;, M. Kadri
2008-01-01
This paper proposes a new objective function and corresponding formulations for the vehicle routing problem. The new cost function defined as the product of the distance of the arc and the flow on that arc. We call a vehicle routing problem with this new objective function as the Cumulative Vehicle Routing Problem (CumVRP). Integer programming formulations with O(n2) binary variables and O(n2) constraints are developed for both collection and delivery cases. We show that the CumVRP is a gener...
Rousseau, Madeleine; Ter Haar, D
1973-01-01
This collection of problems and accompanying solutions provide the reader with a full introduction to physical optics. The subject coverage is fairly traditional, with chapters on interference and diffraction, and there is a general emphasis on spectroscopy.
The Congruence Subgroup Problem
Indian Academy of Sciences (India)
M S Raghunathan
2004-11-01
This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.
Overcoming breastfeeding problems
Plugged milk ducts; Nipple soreness when breastfeeding; Breastfeeding - overcoming problems; Let-down reflex ... no clear cause of nipple soreness. A simple change in your baby's position while feeding may ease ...
Menstruation and Menstrual Problems
... and Menstrual Problems: Condition Information Skip sharing on social media links Share this: Page Content What is menstruation? What is the menstrual cycle? When happens when a pregnancy occurs? What is menstruation? Menstruation (pronounced men-stroo- ...
Institute of Scientific and Technical Information of China (English)
岳科来
2016-01-01
There have considerable number of design philosophies and design methods in this world,but today I’d like to intorduce a new design problem solving system which comes from Chinese traditonal religion Dao.
Nash, Jr, John Forbes
2016-01-01
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
Problems Digesting Dairy Products?
... Consumers Home For Consumers Consumer Updates Problems Digesting Dairy Products? Share Tweet Linkedin Pin it More sharing ... the natural sugar found in milk and other dairy products. People who cannot digest lactose have a ...
Problems, Prospects And Challenges.
African Journals Online (AJOL)
Urban Road Transportation in Nigeria From 1960 To 2006: Problems, Prospects And Challenges. ... Ethiopian Journal of Environmental Studies and Management ... The paper suggested the construction of more motor-able roads within cities ...
... damage your eyes. The most common problem is diabetic retinopathy. It is a leading cause of blindness ... You need a healthy retina to see clearly. Diabetic retinopathy damages the tiny blood vessels inside your ...
... part of an infected walking barefoot, such as swimming pools, nail or the use of over-the-counter ... a chronic problem, your podiatrist may be a history of athlete's foot and can perform a procedure ...
McDonald, James E.
1978-01-01
Several theories and treatments of enuresis are described. The authors conclude that enuresis is a social problem (perhaps due to maturational lag, developmental delay or faulty learning) which requires teacher and parental tolerance and understanding. (SE)
Directory of Open Access Journals (Sweden)
Yen Hung Chen
2012-01-01
minimum cost spanning tree T in G such that the total weight in T is at most a given bound B. In this paper, we present two polynomial time approximation schemes (PTASs for the constrained minimum spanning tree problem.
Wilson, James Q.; And Others
1972-01-01
Argues that most of the underlying assumptions of presently recommended solutions to the problem of heroin addiction are unreasonable, unwarranted, or at least open to more than one interpretation. (DM)
Scheper, W A; Lobbezoo, F; Eijkman, M A J
2005-05-01
Divers can have several oral problems. Firstly, problems caused by pressure changes. These are barodontalgia and odontocrexis. Barodontalgia is toothache by barotrauma. Odontocrexis is restorations coming lose or breaking or tooth fractures by expansion of air beneath restorations. Other problems can occur by cements used to fix casted restorations, by inflammations in the orofacial region, and by not yet fully healed oral wounds. Secondly, there are problems related to the diver's mouthpiece. To keep the mouthpiece in place, the mandible has to be forced in a forward position. Holding this position often and for long periods of time, may develop or aggravate temporomandibular dysfunction. Insufficient fit of the mouthpiece may induce oral mucosal lesions. Therefore, it is recommended to produce individual diver mouthpieces. It is also recommended to produce individual diver mouthpieces for complete dentures wearing divers and for divers with fixed orthodontic appliances.
Heggie, D C
2000-01-01
This didactic paper is motivated by the problem of understanding how stars escape from globular star clusters. One formulation of this problem is known, in dynamical astronomy, as Hill's problem. Originally intended as a model for the motion of the moon around the earth with perturbations by the sun, with simple modifications it also serves as a model for the motion of a star in a star cluster with perturbations by the galaxy. The paper includes introductory sections on the derivation of the equations of motion of Hill's problem, their elementary properties, and extensions to deal with non-point masses and non-circular orbits. We then show how the rate of escape may be calculated numerically and estimated theoretically, and discuss how this simple picture is modified if the stars in a cluster are also undergoing two-body relaxation. Finally we introduce some established ideas for obtaining the distribution of escape times.
Directory of Open Access Journals (Sweden)
Paola Cappola
2014-01-01
Full Text Available In this current work, I am proposing a general close examination of Problem Based Learning as a student centered educational method in which a problem constitutes the starting point of the learning process. Such a method provides students with the suitable knowledge for problem solving and presents numerous and significant differences compared to traditional education.In particular, I analyze the theoretic aspects of problem learning by tracing a history and presenting its structure, clarifying the role of the tutor in the various phases of the learning process. The method has found a wide diffusion since the beginning of the 70s and numerous studies have confirmed the advantages. The effectiveness of PBL is construable and is based on principles of constructivism and cognitivism.
DEFF Research Database (Denmark)
Tietjen, Anne; Jørgensen, Gertrud
2016-01-01
In a time of increasing globalisation and urbanisation, shrinking peripheral rural areas have become a truly wicked planning problem in many European countries. Although a problem can be easily perceived and measured by various indicators, the precise definition of the problem is problematic. Based...... on the case of a Danish planning process which was carried out in collaboration with a charitable trust, this paper discusses an emerging strategic planning approach at the municipal level. We use the concept of wicked problems, strategic planning theory and Actor-Network-Theory to study a collaborative......, place-based and project-oriented process directed at concrete physical outcomes. We frame strategic planning as a translation process where the interaction between human and non-human actors translates a unique, complex and contested situation into an innovated situation. We find that local physical...
Directory of Open Access Journals (Sweden)
Dr Jane Gregory
2016-11-01
Full Text Available Framing ‘science and society’ as a conflict has diverted us from more important problems. Our economic environment urges the commercialisation and social acceptance of new technologies, and science communicators and their publics contribute work to these ends. These activities neglect existing, uncontroversial technologies that, in a collaboration between responsible scientists and their publics, could be deployed to address global problems.
Dubois, Swan; Zhu, Nini
2012-01-01
We investigate the hardness of establishing as many stable marriages (that is, marriages that last forever) in a population whose memory is placed in some arbitrary state with respect to the considered problem, and where traitors try to jeopardize the whole process by behaving in a harmful manner. On the negative side, we demonstrate that no solution that is completely insensitive to traitors can exist, and we propose a protocol for the problem that is optimal with respect to the traitor containment radius.
Schröer, H.
In basketball there is the problem of hitting a basket at a determined distance and a determined height. The quantities that can be changed during the inclined throw are the initial velocity and the angle of throw. At first we neglect the air resistance. Then we treat the same problem in a medium (liquid, gas) with constant density. We obtain two differential equations. Then we view special cases of the retarding force. There is an english and a german edition.
Distributed Storage Allocation Problems
Leong, Derek; Dimakis, Alexandros G.; Ho, Tracey
2009-01-01
We investigate the problem of using several storage nodes to store a data object, subject to an aggregate storage budget or redundancy constraint. It is challenging to find the optimal allocation that maximizes the probability of successful recovery by the data collector because of the large space of possible symmetric and nonsymmetric allocations, and the nonconvexity of the problem. For the special case of probability-l recovery, we show that the optimal allocatio...
2017-03-01
the "SAS+-level Changes" section. Many modern heuristics use a technique called "delete- relaxation ". Delete relaxation does not handle counts and...use the same algorithm, representation, and use the same technique to generate their heuristics. The drawback of this is that there is almost never...one problem solving technique , one representation, or one way to create heuristics that works well on all problems/domains. There is a tradeoff
Hwang, FK; Winter, P
1992-01-01
The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues. This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most...
Bicriteria network design problems
Energy Technology Data Exchange (ETDEWEB)
Marathe, M.V. [Los Alamos National Lab., NM (United States); Ravi, R. [Princeton Univ., NJ (United States); Sundaram, R. [Massachusetts Inst. of Tech., Cambridge, MA (United States); Ravi, S.S.; Rosenkrantz, D.J.; Hunt, H.B. III [State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
1997-11-20
The authors study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a subgraph from a given subgraph class that minimizes the second objective subject to the budget on the first. They consider three different criteria -- the total edge cost, the diameter and the maximum degree of the network. Here, they present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, they develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same they present a black box parametric search technique. This black box takes in as input an (approximation) algorithm for the criterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs they use a cluster based approach to devise approximation algorithms. The solutions violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, they provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. The authors show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.
Colored Traveling Salesman Problem.
Li, Jun; Zhou, MengChu; Sun, Qirui; Dai, Xianzhong; Yu, Xiaolong
2015-11-01
The multiple traveling salesman problem (MTSP) is an important combinatorial optimization problem. It has been widely and successfully applied to the practical cases in which multiple traveling individuals (salesmen) share the common workspace (city set). However, it cannot represent some application problems where multiple traveling individuals not only have their own exclusive tasks but also share a group of tasks with each other. This work proposes a new MTSP called colored traveling salesman problem (CTSP) for handling such cases. Two types of city groups are defined, i.e., each group of exclusive cities of a single color for a salesman to visit and a group of shared cities of multiple colors allowing all salesmen to visit. Evidences show that CTSP is NP-hard and a multidepot MTSP and multiple single traveling salesman problems are its special cases. We present a genetic algorithm (GA) with dual-chromosome coding for CTSP and analyze the corresponding solution space. Then, GA is improved by incorporating greedy, hill-climbing (HC), and simulated annealing (SA) operations to achieve better performance. By experiments, the limitation of the exact solution method is revealed and the performance of the presented GAs is compared. The results suggest that SAGA can achieve the best quality of solutions and HCGA should be the choice making good tradeoff between the solution quality and computing time.
Chou, Kai-Seng
2001-01-01
Although research in curve shortening flow has been very active for nearly 20 years, the results of those efforts have remained scattered throughout the literature. For the first time, The Curve Shortening Problem collects and illuminates those results in a comprehensive, rigorous, and self-contained account of the fundamental results.The authors present a complete treatment of the Gage-Hamilton theorem, a clear, detailed exposition of Grayson''s convexity theorem, a systematic discussion of invariant solutions, applications to the existence of simple closed geodesics on a surface, and a new, almost convexity theorem for the generalized curve shortening problem.Many questions regarding curve shortening remain outstanding. With its careful exposition and complete guide to the literature, The Curve Shortening Problem provides not only an outstanding starting point for graduate students and new investigations, but a superb reference that presents intriguing new results for those already active in the field.
[Halitosis. A common problem].
Laine, M L; Slot, D E; Danser, M M
2011-12-01
Halitosis is a frequently occurring problem, the cause of which is generally to be found in the mouth. The challenge for oral health care providers is to diagnose it correctly and treat it effectively. Differential diagnosis is of great importance in making a distinction between halitosis which originates in the mouth and which does not originate in the mouth. Oral halitosis can be treated effectively by good oral health care. Plaque accumulation on the tongue is the most common cause of oral halitosis. Tongue cleansing, possibly in combination with a specific mouth wash, is consequently recommended as an element of oral hygiene care. Other oral health problems, such as periodontal disease, caries and ill-fitting removable dentures should be treated adequately to eliminate these problems as potential causes of halitosis.
Solved problems in electromagnetics
Salazar Bloise, Félix; Bayón Rojo, Ana; Gascón Latasa, Francisco
2017-01-01
This book presents the fundamental concepts of electromagnetism through problems with a brief theoretical introduction at the beginning of each chapter. The present book has a strong didactic character. It explains all the mathematical steps and the theoretical concepts connected with the development of the problem. It guides the reader to understand the employed procedures to learn to solve the exercises independently. The exercises are structured in a similar way: The chapters begin with easy problems increasing progressively in the level of difficulty. This book is written for students of physics and engineering in the framework of the new European Plans of Study for Bachelor and Master and also for tutors and lecturers. .
Energy Technology Data Exchange (ETDEWEB)
Sivertsen, B.
1995-09-01
This document focuses on the specific problems of urban air pollution related to emissions, urban climate, meteorology, smog potential, specific locations, air pollution measurements and trends. Examples are given with cases from European cities in particular. The north south differences, coastal and inland problems and data from various parts of Europe are presented. Global trends and results from the UNEP programme are used to illustrate the magnitude of the problem. Special emphasis is placed on the impact of different sources and their importance in selected cities. Different types of atmospheric dispersion models, their development and use, is outlined. The importance of local and regional meteorological data for explanation purposes and for estimating and forecasting urban air quality is presented. Finally, monitoring programmes, mapping, impact assessment and optimum abatement strategy planning are illustrated with examples from different areas in the world. 9 refs., 56 figs., 1 table
Computational problems in engineering
Mladenov, Valeri
2014-01-01
This book provides readers with modern computational techniques for solving variety of problems from electrical, mechanical, civil and chemical engineering. Mathematical methods are presented in a unified manner, so they can be applied consistently to problems in applied electromagnetics, strength of materials, fluid mechanics, heat and mass transfer, environmental engineering, biomedical engineering, signal processing, automatic control and more. • Features contributions from distinguished researchers on significant aspects of current numerical methods and computational mathematics; • Presents actual results and innovative methods that provide numerical solutions, while minimizing computing times; • Includes new and advanced methods and modern variations of known techniques that can solve difficult scientific problems efficiently.
Revisiting the Lambert's Problem
Izzo, Dario
2014-01-01
The orbital boundary value problem, also known as Lambert Problem, is revisited. Building upon Lancaster and Blanchard approach, new relations are revealed and a new variable representing all problem classes, under L-similarity, is used to express the time of flight equation. In the new variable, the time of flight curves have two oblique asymptotes and they mostly appear to be conveniently approximated by piecewise continuous lines. We use and invert such a simple approximation to provide an efficient initial guess to an Householder iterative method that is then able to converge, for the single revoltuion case, in only two iterations. The resulting algorithm is compared to Gooding's procedure revealing to be numerically as accurate, while having a smaller computational complexity.
A Survey of Transportation Problems
2014-01-01
This paper aims at being a guide to understand the different types of transportation problems by presenting a survey of mathematical models and algorithms used to solve different types of transportation modes (ship, plane, train, bus, truck, Motorcycle, Cars, and others) by air, water, space, cables, tubes, and road. Some problems are as follows: bus scheduling problem, delivery problem, combining truck trip problem, open vehicle routing problem, helicopter routing problem, truck loading p...
Electric circuits problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av
Matrices in Engineering Problems
Tobias, Marvin
2011-01-01
This book is intended as an undergraduate text introducing matrix methods as they relate to engineering problems. It begins with the fundamentals of mathematics of matrices and determinants. Matrix inversion is discussed, with an introduction of the well known reduction methods. Equation sets are viewed as vector transformations, and the conditions of their solvability are explored. Orthogonal matrices are introduced with examples showing application to many problems requiring three dimensional thinking. The angular velocity matrix is shown to emerge from the differentiation of the 3-D orthogo
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The pricing of electricity trasmission requires determining how much use each generator is making of a transmission line and what is each generator's contribution to the system losses. Such problems cannot be solved by only using Kirchoff's laws. This paper proposes two current decomposition axioms based on which the theories and models are established for the current trace problem. To create an efficient algorithm the graph theory is employed. It is proved that there is no directed circuit in a directed current distribution graph. According to this theorem a very simple and efficient algorithm based on recursive elimination process is suggested. A simple example is used to explain the algorithm.
Calculus problems and solutions
Ginzburg, A
2011-01-01
Ideal for self-instruction as well as for classroom use, this text helps students improve their understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. More than 1,200 problems appear in the text, with concise explanations of the basic notions and theorems to be used in their solution. Many are followed by complete answers; solutions for the others appear at the end of the book. Topics include sequences, functions of a single variable, limit of a function, differential calculus for functions of a single variable, fundamental theorems and applications of dif
Advanced calculus problem solver
REA, Editors of
2012-01-01
Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av
Problems in classical mechanics
Katkar, L N
2014-01-01
Problems in classical mechanics presents a lucid treatment of the formulations of Lagrangian, Hamiltonian, and the Principles of Calculus of Variations etc. important for the study of modern physics. The study of classical mechanics prepares students to apply the principles and the mathematical tools to solve real life problems. The book also incorporates and discusses in detail topics such as Central Force Motion, Rigid Body Motion and Canonical Transformations. KEY FEATURES: Around 200 solved examples with complete mathematical theory Around 70 examples given as an exercise to test and develop students understanding The physical interpretation of the Hamiltonian is highlighted
Problems over Information Systems
Chikalov, Igor
2011-01-01
The problems of estimation of the minimum average time complexity of decision trees and design of efficient algorithms are complex in general case. The upper bounds described in Chap. 2.4.3 can not be applied directly due to large computational complexity of the parameter M(z). Under reasonable assumptions about the relation of P and NP, there are no polynomial time algorithms with good approximation ratio [12, 32]. One of the possible solutions is to consider particular classes of problems and improve the existing results using characteristics of the considered classes. © Springer-Verlag Berlin Heidelberg 2011.
Kogan, VI; Gersch, Harold
2011-01-01
Written by a pair of distinguished Soviet mathematicians, this compilation presents 160 lucidly expressed problems in nonrelativistic quantum mechanics plus completely worked-out solutions. Some were drawn from the authors' courses at the Moscow Institute of Engineering, but most were prepared especially for this book. A high-level supplement rather than a primary text, it constitutes a masterful complement to advanced undergraduate and graduate texts and courses in quantum mechanics.The mathematics employed in the proofs of the problems-asymptotic expansions of functions, Green's functions, u
Minimal Controllability Problems
Olshevsky, Alex
2013-01-01
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the minimum number of variables that need to be affected within a multiplicative factor of $c \\log n$ is NP-hard for some positive $c$. On the positive side, we show it is possible to find sets of variables matching this inapproximability barrier in polynomial time....
Classic Problems of Probability
Gorroochurn, Prakash
2012-01-01
"A great book, one that I will certainly add to my personal library."—Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature. From Cardano's 1564 Games of Chance to Jacob Bernoulli's 1713 Golden Theorem to Parrondo's 1996 Perplexin
DEFF Research Database (Denmark)
Reng, Lars; Schoenau-Fog, Henrik
2011-01-01
At Aalborg University’s department of Medialogy, we are utilizing the Problem Based Learning method to encourage students to solve game design problems by pushing the boundaries and designing innovative games. This paper is concerned with describing this method, how students employ it in various...... projects and how they learn to analyse, design, and develop for innovation by using it. We will present various cases to exemplify the approach and focus on how the method engages students and aspires for innovation in digital entertainment and games....
DEFF Research Database (Denmark)
Ovesen, Nis
2015-01-01
Problem-based learning (PBL) is becoming increasingly popular in design educations, but how is it taught and practiced? This paper presents a case study of a three-day workshop that has the purpose of introducing PBL to design students. A theoretical background on PBL and problems in design...... is established and is backing up the case study. The study shows that design engineering and architectural students without experience in PBL in general finds the approach to be beneficial when working on a design challenge in a student team....
DEFF Research Database (Denmark)
Reng, Lars; Schoenau-Fog, Henrik
2011-01-01
At Aalborg University’s department of Medialogy, we are utilizing the Problem Based Learning method to encourage students to solve game design problems by pushing the boundaries and designing innovative games. This paper is concerned with describing this method, how students employ it in various...... projects and how they learn to analyse, design, and develop for innovation by using it. We will present various cases to exemplify the approach and focus on how the method engages students and aspires for innovation in digital entertainment and games....
Pratelli, Aldo
2016-01-01
This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.
Aeroelastic problems in turbomachines
Bendiksen, Oddvar O.
1993-01-01
An overview is given of aeroelastic problems in turbomachines, emphasizing recent research. Unsteady flow in cascade and turbomachinery rotors is discussed, including supersonic and transonic linearized potential flow and nonlinear flow models. Computational and modeling aspects of the flutter of fan and compressor blades are examined. The correlation of the findings with experimental data is considered. Future directions in turbomachinery aeroelasticity are addressed.
DEFF Research Database (Denmark)
Janstrup, Kira; Rose, Trine Høyer; Andersen, Kent Høj
. In addition to our project two other projects are made where an optimal solution to the container stowage problem also is tried to be found, but by using constraint programming and local search instead respectively. We will therefore in the end compare these three methods and the achieved results on fastness...
Problem Solving Using Microcomputers.
Demana, Franklin; Waits, Bert
1987-01-01
It is argued that microcomputer technology has evolved to the stage that it should be routinely used by mathematics students at all levels. It is shown how the use of microcomputers can change the way problems are solved. Computer-generated graphics are highlighted. (PK)
Solving Problems through Circles
Grahamslaw, Laura; Henson, Lisa H.
2015-01-01
Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…
Managing soil remediation problems.
Okx, J P; Hordijk, L; Stein, A
1996-12-01
Soil remediation has only a short history but the problem addressed is a significant one. Cost estimates for the clean-up of contaminated sites in the European Union and the United States are in the order of magnitude of 1,400 billion ECU. Such an enormous operation deserves the best management it can get. Reliable cost estimations per contaminated site are an important prerequisite. This paper addresses the problems related to site-wise estimations.When solving soil remediation problems, we have to deal with a large number of scientific disciplines. Too often solutions are presented from the viewpoint of only one discipline. In order to benefit from the combined disciplinary knowledge and experience, we think that it is necessary to describe the interrelations between these disciplines. This can be realized by developing an adequate model of the desired process which enables to consider and evaluate the essential factors as interdependent components of the total system.The resulting model provides a binding paradigm to the contributing disciplines which will result in improved efficiency and effectivity of the decision and the cost estimation process. In the near future, we will release the "Biosparging and Bioventing Expert Support System", an expert support system for problem owners, consultants and authorities dealing with the design and operation of a biosparging and/or a bioventing system.
Solving Problems through Circles
Grahamslaw, Laura; Henson, Lisa H.
2015-01-01
Several problem-solving interventions that utilise a "circle" approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. This research explored two interventions, Solution Circles and Circle of Adults, and used thematic…
Olson, Alton T.
1993-01-01
Presents a series of solution methods to the Eight Queens Problem of placing eight queens on a chess board so that no one queen can capture another. Solution methods progress from empirical approaches to the use of computer algorithms. Geometric transformations are used to find other solutions. (MDH)
Environmental Health Problems.
Environmental Health Service (DHEW/PHS), Rockville, MD.
Aimed at a society which is forced to make decisions relative to their total environment, this pamphlet discusses a few of the problems associated with restoring and maintaining an environmental relationship conducive to the health and well-being of man. The topics covered include: air pollution, noise, solid waste, the urban environment, drinking…
DEFF Research Database (Denmark)
Tietjen, Anne; Jørgensen, Gertrud
2016-01-01
projects played a major role in this process. First, they acted as a vehicle that assembled planners, politicians and stakeholders to work towards strategic visions across multiple scales. Second and consequently, they stimulated considerable second and third order effects in the form of shared problem...
The Vehicle Rescheduling Problem
R. Spliet (Remy); A.F. Gabor (Adriana); R. Dekker (Rommert)
2009-01-01
textabstractThe capacitated vehicle routing problem is to find a routing schedule describing the order in which geographically dispersed customers are visited to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. In many practical applications, a long
Emmel, Thomas C.; Sligh, Michael M.
1970-01-01
Asserts that overpopulation is the most pressing world problem. Topics discussed include population control in primitive societies, population growth and control in modern societies, methods of motivational population control, consequences of no population control, and mass famines during the 1970's in underdeveloped countries. Cities 33…
Emmel, Thomas C.; Sligh, Michael M.
1970-01-01
Asserts that overpopulation is the most pressing world problem. Topics discussed include population control in primitive societies, population growth and control in modern societies, methods of motivational population control, consequences of no population control, and mass famines during the 1970's in underdeveloped countries. Cities 33…
Universal Design Problem Solving
Sterling, Mary C.
2004-01-01
Universal design is made up of four elements: accessibility, adaptability, aesthetics, and affordability. This article addresses the concept of universal design problem solving through experiential learning for an interior design studio course in postsecondary education. Students' experiences with clients over age 55 promoted an understanding of…
Postoperative upper airway problems
African Journals Online (AJOL)
QuickSilver
2003-06-09
Jun 9, 2003 ... REVIEW ARTICLE. Southern African Journal of Anaesthesia & Analgesia - May 2003. 12. Postoperative upper airway problems way. A number of factors, some avoidable, influence the incidence ... debilitating pain, inability to swallow and temporary voice changes, and are a ..... decrease airway resistance.
The information recovery problem
Baccetti, Valentina; Terno, Daniel R
2016-01-01
The problem of rescuing unitary matter evolution on a black hole spacetime remains unresolved. We argue that some prominent cures are more troubling than the disease, demonstrate that their central element --- forming of the event horizon before the evaporation begins --- is not necessarily true, and describe a fully coupled matter-gravity system which is manifestly unitary.
De Bono, Edward
A group of children were presented with several tasks, including the invention of a sleep machine and a machine to weigh elephants. The tasks were chosen to involve the children in coping with problems of a distinct character. A study of the children's drawings and interpretations shows that children's thinking ability is not very different from…
Institute of Scientific and Technical Information of China (English)
刘香情; 钱丹
2002-01-01
With the population growing, a lot of problems have come out, Nowadays a lot of tall buildings have been built, but the houses are still very short; A lot of cars and buses have increased, but they are still crowded with people; A lot of schools have been built,
Naboulsi, R
2003-01-01
A review on CP violation in the B and K mesons systems is given, which, we hope may familiarize new Belle members in the basic ingredients of this topic, which is one of the most challenging problems of experimental high energy physics.
Currier, Sarah Cox
2015-01-01
In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…
Team Learning on Messy Problems
Rouwette, E.A.J.A.; Vennix, J.A.M.
2007-01-01
Concentrates on procedures used to foster group learning for a particular type of problem, the so-called messy problem. The distinctive feature of messy problems is that the people involved have different ideas on what the problem is or whether there even is a problem. Nevertheless, those involved
Team Learning on Messy Problems
Rouwette, E.A.J.A.; Vennix, J.A.M.
2007-01-01
Concentrates on procedures used to foster group learning for a particular type of problem, the so-called messy problem. The distinctive feature of messy problems is that the people involved have different ideas on what the problem is or whether there even is a problem. Nevertheless, those involved i
A model for routing problem in quay management problem
Zirour, Mourad; Oughalime, Ahmed; Liong, Choong-Yeun; Ismail, Wan Rosmanira; Omar, Khairuddin
2014-06-01
Quadratic Assignment Problem (QAP), like Vehicle Routing Problem, is one of those optimization problems that interests many researchers in the last decades. The Quay Management Problem is a specific problem which could be presented as a QAP which involves a double assignment of customers and products toward loading positions using lifting trucks. This study focuses on the routing problem while delivering the customers' demands. In this problem, lifting trucks will route around the storage sections to collect the products then deliver to the customers who are assigned to specific loading positions. The objective of minimizing the residence time for each customer is sought. This paper presents the problem and the proposed model.
How to solve mathematical problems
Wickelgren, Wayne A
1995-01-01
Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Heuristics for Multidimensional Packing Problems
DEFF Research Database (Denmark)
Egeblad, Jens
In this thesis we consider solution methods for packing problems. Packing problems occur in many different situations both directly in the industry and as sub-problems of other problems. High-quality solutions for problems in the industrial sector may be able to reduce transportation and production...... costs significantly. For packing problems in general are given a set of items and one of more containers. The items must be placed within the container such that some objective is optimized and the items do not overlap. Items and container may be rectangular or irregular (e.g. polygons and polyhedra...... methods. Two important problem variants are the knapsack packing problem and the strip-packing problem. In the knapsack packing problem, each item is given a profit value, and the problem asks for the subset with maximal profit that can be placed within one container. The strip-packing problem asks...
No Problem? No Research, Little Learning ... Big Problem!
Directory of Open Access Journals (Sweden)
Fernando Ornelas Marques
2012-06-01
Full Text Available The motivation to carry out this study stemmed from the generalized perception that nowadays youth lacks the skills for the 21st century. Especially the high-level competences like critical thinking, problem solving and autonomy. Several tools can help to improve these competences (e.g. the SCRATCH programming language, but, as researchers and educators, we are mostly concerned with the skill to recognize problems. What if we do not find problems to solve? What if we do not even feel the need to find or solve problems? The problem is to recognize the problem; the next step is to equate the problem; finally we have to feel the need to solve it. No need? No invention. Recognizing a problem is probably the biggest problem of everyday life, because we are permanently faced with problems (many ill-defined problems, which we need to identify, equate and solve.
No Problem? No Research, Little Learning ... Big Problem!
Directory of Open Access Journals (Sweden)
Fernando Ornelas Marques
2012-06-01
Full Text Available The motivation to carry out this study stemmed from the generalized perception that nowadays youth lacks the skills for the 21st century. Especially the high-level competences like critical thinking, problem solving and autonomy. Several tools can help to improve these competences (e.g. the SCRATCH programming language, but, as researchers and educators, we are mostly concerned with the skill to recognize problems. What if we do not find problems to solve? What if we do not even feel the need to find or solve problems? The problem is to recognize the problem; the next step is to equate the problem; finally we have to feel the need to solve it. No need? No invention. Recognizing a problem is probably the biggest problem of everyday life, because we are permanently faced with problems (many ill-defined problems, which we need to identify, equate and solve.
Scattering problems in elastodynamics
Diatta, Andre; Kadic, Muamer; Wegener, Martin; Guenneau, Sebastien
2016-09-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this Rapid Communication, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasistatic regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
Scattering problems in elastodynamics
Diatta, Andre; Wegener, Martin; Guenneau, Sebastien
2016-01-01
In electromagnetism, acoustics, and quantum mechanics, scattering problems can routinely be solved numerically by virtue of perfectly matched layers (PMLs) at simulation domain boundaries. Unfortunately, the same has not been possible for general elastodynamic wave problems in continuum mechanics. In this paper, we introduce a corresponding scattered-field formulation for the Navier equation. We derive PMLs based on complex-valued coordinate transformations leading to Cosserat elasticity-tensor distributions not obeying the minor symmetries. These layers are shown to work in two dimensions, for all polarizations, and all directions. By adaptative choice of the decay length, the deep subwavelength PMLs can be used all the way to the quasi-static regime. As demanding examples, we study the effectiveness of cylindrical elastodynamic cloaks of the Cosserat type and approximations thereof.
DEFF Research Database (Denmark)
de Graaff, Erik; Guerra, Aida
, the key principles remain the same everywhere. Graaff & Kolmos (2003) identify the main PBL principles as follows: 1. Problem orientation 2. Project organization through teams or group work 3. Participant-directed 4. Experiental learning 5. Activity-based learning 6. Interdisciplinary learning and 7......Problem-Based Learning (PBL) is an innovative method to organize the learning process in such a way that the students actively engage in finding answers by themselves. During the past 40 years PBL has evolved and diversified resulting in a multitude in variations in models and practices. However....... Exemplary practice. The University of Aalborg in Denmark started with PBL right from the start when the school was founded merging several educational institutes in Northern Denmark in 1974. The Aalborg PBL model is recognized around the world as an example or a source of inspiration, in particular...
The Boolean Isomorphism problem
Energy Technology Data Exchange (ETDEWEB)
Agrawal, M. [Indian Institute of Technology, Kanpur (India); Thierauf, T. [Universitaet Ulm (Germany)
1996-12-31
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be {sigma}{sup p}{sub 2} complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And- and Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.
Institute of Scientific and Technical Information of China (English)
王锡凡; 王秀丽
2000-01-01
The pricing of electricity trasmission requires determining how much use each generator is making of a transmission line and what is each generator’s contribution to the system losses. Such problems cannot be solved by only using Kirchoff’s laws. This paper proposes two current decomposition axioms based on which the theories and models are established for the current trace problem. To create an efficient algorithm the graph theory is employed. It is proved that there is no directed circuit in a directed current distribution graph. According to this theorem a very simple and efficient algorithm based on recursive elimination process is suggested. A simple example is used to explain the algorithm .
Medical problems in pregnancy.
Narayan, Bhaskar; Nelson-Piercy, Catherine
2016-12-01
The prevalence of medical problems in pregnancy is increasing because of a complex interplay between demographic and lifestyle factors, and developments in modern medicine. Maternal mortality and morbidity resulting from treatable medical conditions, such as venous thromboembolism, epilepsy and autoimmune disease, have not decreased in recent years. This is despite a marked decrease in overall maternal mortality. It is vital that all physicians acquire a basic knowledge and understanding of medical problems in pregnancy. This includes prepregnancy measures such as counselling and optimisation of medical therapy, as well as multidisciplinary management throughout pregnancy and the postpartum period. Prompt recognition and treatment of acute and chronic illness is of clear benefit, and most drugs and many radiological investigations may be used in pregnancy.
Directory of Open Access Journals (Sweden)
Pešić Jelena M.
2005-01-01
Full Text Available This paper deals with various reasons for treating the problematisation of textbook discourse as an important aspect of its educational design. These reasons are derived from: the nature of learning process, the nature of scientific knowledge and both motivational and cognitive saint achieved through a problematisation of learning material. Implications drawn from these considerations, along with textbook genre possibilities and constrains, lead us to define some basic strategies of textbook discourse problematisation. They refer to: way of presenting knowledge (problem structuring of text, presenting the history of knowledge and different perspectives; use of specific questions and tasks; metacognitive support of the learning process and specific type of textbook language (dialogical problem focused, language of thinking.
Problems in Cybersemiotic Modelling
DEFF Research Database (Denmark)
Brier, Søren
2014-01-01
the Peircean theory of the observer as the phaneroscopic foundation. 4. Cobley points out that both models, as they are combined in Cybersemiotics lacks to integrate a theory of interest and power. They are too consensual in their view on communication. This is a general problem in both theories. Still Luhmann......Going from an empirical to an informational paradigm of cognition and communication, does not really help us to analyze, how the living systems manage to make a meaningful interpretation of environment that is useful for their survival and procreation. Other models are needed. 1. There is von...... Uexküll’s cybernetic-behavioral model, which has the problem of being placed in a Platonic, static worldview. The Umwelt of an animal is a construction limited of its functional realism of survival. It is connected to the species. 2. Ture von Uexküll and Søren Brier both realized that Maturana and Varela...
Enumula, Prabodh K
2008-01-01
This paper proposes the Potluck Problem as a model for the behavior of independent producers and consumers under standard economic assumptions. We model this by using resource allocation in a multi-agent system in which there is no explicit communication among the agents. The model proposed has many applications in modeling systems like electrical power grids with many consumers and producers, service-on-demand in grid computing and peer-to-peer computing environments, maintaining a good ratio between demand and inventory in supply chain management, etc. It is observed that a rational learning approach is unable to achieve equilibrium or near-equilibrium in the Potluck Problem. Instead, a weighted majority learning algorithm is applied, which does much better in maintaining parity of supply and demand in varying-demand situations.
1979-01-01
The corrosion problem, it turned out, stemmed from the process called electrolysis. When two different metals are in contact, an electrical potential is set up between them; when the metals are surrounded by an electrolyte, or a conducting medium, the resulting reaction causes corrosion, often very rapid corrosion. In this case the different metals were the copper grounding system and the ferry's aluminum hull; the dockside salt water in which the hull was resting served as the electrolyte. After identifying the source of the trouble, the Ames engineer provided a solution: a new wire-and-rod grounding system made of aluminum like the ferry's hull so there would no longer be dissimilar metals in contact. Ames research on the matter disclosed that the problem was not unique to the Golden Gate ferries. It is being experienced by many pleasure boat operators who are probably as puzzled about it as was the Golden Gate Transit Authority.
DEFF Research Database (Denmark)
Hansen, David
2012-01-01
employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?” The research project was carried out as a co-creation process with close cooperation between researcher......Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage...... and participants and was documented by qualitative methods. This paper presents an academic literature review on Appreciative Inquiry and problem solving for continuous improvements that did not reveal successful attempts in combining the two.Both the literature and the empirical study showed one of the main...
CHIH HSUN HSIEH
2011-01-01
The work presented in this paper has been motivated primarily by Zadeh's idea of linguistic variables intended to provide rigorous mathematical modeling of natural language and CWW, Computing With Words. This paper reports some modeling of the linguistic inventory problems where CWW have been implemented: linguistic production inventory, linguistic inventory models under linguistic demand and linguistic lead time, linguistic production inventory models based on the preference of a decision ma...
2016-07-22
techniques and the use of sphere packing results in analyzing the performance of the two approximation algorithms may also find other applications in...problem in 2-D networks. We then develop two polynomial-time approximation algorithms that offer and approximation ratios for general directed hypergraphs...eavesdropperswitharbitraryunknownloca- tions (the so-called1.5-Dnetworks).Weproposea linear-complexity algorithm based on nested backward induction that obtains the op- timal solution
Creativity and problem Solving
Directory of Open Access Journals (Sweden)
René Victor Valqui Vidal
2004-12-01
Full Text Available This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools.
Europeanisation: Solution or problem?
Directory of Open Access Journals (Sweden)
Claudio M. Radaelli
2004-10-01
Full Text Available Is there something new in recent research on Europeanisation? Or should we go back to what we already know about political integration in Europe and avoid the term? This article reviews recent work in four steps: the identification of the specific domain of Europeanisation; the relationship between Europeanisation, on the one hand, and governance, institutions, and discourse, on the other; the methodological problems and the models emerging in this new field of research; and an assessment of the results arising out of theoretical and empirical research. One theme throughout the article is that, in order to develop a progressive agenda, Europeanisation should be seen as a problem, not as a solution. It is neither a new theory, nor an ad-hoc approach. Rather, it is a way of orchestrating existing concepts and to contribute to cumulative research in political science. Europeanisation does not provide any simple fix to theoretical or empirical problems. Quite the opposite, it can deliver if approached as a set of puzzles. A problem in search of explanation not the explanation itself (Gualini 2003. The conclusion is that Europeanisation has contributed to the emergence of new insights, original explanations, and interesting questions on three important issues: the understanding and analysis of 'impact', how to endogeneise international governance in models of domestic politics, and the relationship between agency and change. These three issues are prominent in the research agendas of international relations, theoretical policy analysis, and comparative politics. To contribute to major issues at the core of political science is a valuable result for a relatively new field of inquiry.
Martinez-Camara, Marta; Dokmanic, Ivan; Ranieri, Juri; Scheibler, Robin; Vetterli, Martin; STOHL Andreas
2013-01-01
Knowing what amount of radioactive material was released from Fukushima in March 2011 and at what time instants is crucial to assess the risk, the pollution, and to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches have relied on a detailed expert guess of how the relea...
Localized Geometric Query Problems
Augustine, John; Maheshwari, Anil; Nandy, Subhas C; Roy, Sasanka; Sarvattomananda, Swami
2011-01-01
A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.
Gol'dman, I I
2010-01-01
A comprehensive collection of problems of varying degrees of difficulty in nonrelativistic quantum mechanics, with answers and completely worked-out solutions. Among the topics: one-dimensional motion, transmission through a potential barrier, commutation relations, angular momentum and spin, and motion of a particle in a magnetic field. An ideal adjunct to any textbook in quantum mechanics, useful in courses in atomic and nuclear physics, mathematical methods in physics, quantum statistics and applied differential equations. 1961 edition.
Creativity and Problem Solving
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2004-01-01
This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...... approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools....
Hansen, David
2012-01-01
Many industrial production work systems have increased in complexity, and their new business model scompete on innovation, rather than low cost.At a medical device production facility committed to Lean Production, a research project was carried out to use Appreciative Inquiry to better engage employee strengths in continuou simprovements of the work system. The research question was: “How can Lean problem solving and Appreciative Inquiry be combined for optimized work system innovation?”The r...
Creativity and Problem Solving
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
2004-01-01
This paper presents some modern and interdisciplinary concepts about creativity and creative processes of special relevance for Operational Research workers. Central publications in the area Creativity-Operational Research are shortly reviewed. Some creative tools and the Creative Problem Solving...... approach are also discussed. Finally, some applications of these concepts and tools are outlined. Some central references are presented for further study of themes related to creativity or creative tools....
Directory of Open Access Journals (Sweden)
Mao-Che Wang
2005-08-01
Full Text Available Acute diffuse otitis externa (swimmer's ear, otomycosis, exostoses, traumatic eardrum perforation, middle ear infection, and barotraumas of the inner ear are common problems in swimmers and people engaged in aqua activities. The most common ear problem in swimmers is acute diffuse otitis externa, with Pseudomonas aeruginosa being the most common pathogen. The symptoms are itching, otalgia, otorrhea, and conductive hearing loss. The treatment includes frequent cleansing of the ear canal, pain control, oral or topical medications, acidification of the ear canal, and control of predisposing factors. Swimming in polluted waters and ear-canal cleaning with cotton-tip applicators should be avoided. Exostoses are usually seen in people who swim in cold water and present with symptoms of accumulated debris, otorrhea and conductive hearing loss. The treatment for exostoses is transmeatal surgical removal of the tumors. Traumatic eardrum perforations may occur during water skiing or scuba diving and present with symptoms of hearing loss, otalgia, otorrhea, tinnitus and vertigo. Tympanoplasty might be needed if the perforations do not heal spontaneously. Patients with chronic otitis media with active drainage should avoid swimming, while patients who have undergone mastoidectomy and who have no cavity problems may swim. For children with ventilation tubes, surface swimming is safe in a clean, chlorinated swimming pool. Sudden sensorineural hearing loss and some degree of vertigo may occur after diving because of rupture of the round or oval window membrane.
Ruskey, Frank; Williams, Aaron
In the classic Josephus problem, elements 1, 2,...,n are placed in order around a circle and a skip value k is chosen. The problem proceeds in n rounds, where each round consists of traveling around the circle from the current position, and selecting the kth remaining element to be eliminated from the circle. After n rounds, every element is eliminated. Special attention is given to the last surviving element, denote it by j. We generalize this popular problem by introducing a uniform number of lives ℓ, so that elements are not eliminated until they have been selected for the ℓth time. We prove two main results: 1) When n and k are fixed, then j is constant for all values of ℓ larger than the nth Fibonacci number. In other words, the last surviving element stabilizes with respect to increasing the number of lives. 2) When n and j are fixed, then there exists a value of k that allows j to be the last survivor simultaneously for all values of ℓ. In other words, certain skip values ensure that a given position is the last survivor, regardless of the number of lives. For the first result we give an algorithm for determining j (and the entire sequence of selections) that uses O(n 2) arithmetic operations.
Quantum Counterfeit Coin Problems
Iwama, Kazuo; Raymond, Rudy; Teruyama, Junichi
2010-01-01
The counterfeit coin problem requires us to find all false coins from a given bunch of coins using a balance scale. We assume that the balance scale gives us only ``balanced'' or ``tilted'' information and that we know the number k of false coins in advance. The balance scale can be modeled by a certain type of oracle and its query complexity is a measure for the cost of weighing algorithms (the number of weighings). In this paper, we study the quantum query complexity for this problem. Let Q(k,N) be the quantum query complexity of finding all k false coins from the N given coins. We show that for any k and N such that k < N/2, Q(k,N)=O(k^{1/4}), contrasting with the classical query complexity, \\Omega(k\\log(N/k)), that depends on N. So our quantum algorithm achieves a quartic speed-up for this problem. We do not have a matching lower bound, but we show some evidence that the upper bound is tight: any algorithm, including our algorithm, that satisfies certain properties needs \\Omega(k^{1/4}) queries.
Wang, Mao-Che; Liu, Chia-Yu; Shiao, An-Suey; Wang, Tyrone
2005-08-01
Acute diffuse otitis externa (swimmer's ear), otomycosis, exostoses, traumatic eardrum perforation, middle ear infection, and barotraumas of the inner ear are common problems in swimmers and people engaged in aqua activities. The most common ear problem in swimmers is acute diffuse otitis externa, with Pseudomonas aeruginosa being the most common pathogen. The symptoms are itching, otalgia, otorrhea, and conductive hearing loss. The treatment includes frequent cleansing of the ear canal, pain control, oral or topical medications, acidification of the ear canal, and control of predisposing factors. Swimming in polluted waters and ear-canal cleaning with cotton-tip applicators should be avoided. Exostoses are usually seen in people who swim in cold water and present with symptoms of accumulated debris, otorrhea and conductive hearing loss. The treatment for exostoses is transmeatal surgical removal of the tumors. Traumatic eardrum perforations may occur during water skiing or scuba diving and present with symptoms of hearing loss, otalgia, otorrhea, tinnitus and vertigo. Tympanoplasty might be needed if the perforations do not heal spontaneously. Patients with chronic otitis media with active drainage should avoid swimming, while patients who have undergone mastoidectomy and who have no cavity problems may swim. For children with ventilation tubes, surface swimming is safe in a clean, chlorinated swimming pool. Sudden sensorineural hearing loss and some degree of vertigo may occur after diving because of rupture of the round or oval window membrane.
Wang, Frédéric
2010-01-01
We give an overview of the Hidden Subgroup Problem (HSP) as of July 2010, including new results discovered since the survey of arXiv:quant-ph/0411037v1. We recall how the problem provides a framework for efficient quantum algorithms and present the standard methods based on coset sampling. We study the Dihedral and Symmetric HSPs and how they relate to hard problems on lattices and graphs. Finally, we conclude with the known solutions and techniques, describe connections with efficient algorithms as well as miscellaneous variants of HSP. We also bring various contributions to the topic. We show that in theory, we can solve HSP over a given group inductively: the base case is solving HSP over its simple factor groups and the inductive step is building efficient oracles over a normal subgroup N and over the factor group G/N. We apply this analysis to the Dedekindian HSP to get an alternative abelian HSP algorithm based on a change of the underlying group. We also propose a quotient reduction by the normal group...
Random eigenvalue problems revisited
Indian Academy of Sciences (India)
S Adhikari
2006-08-01
The description of real-life engineering structural systems is associated with some amount of uncertainty in specifying material properties, geometric parameters, boundary conditions and applied loads. In the context of structural dynamics it is necessary to consider random eigenvalue problems in order to account for these uncertainties. Within the engineering literature, current methods to deal with such problems are dominated by approximate perturbation methods. Some exact methods to obtain joint distribution of the natural frequencies are reviewed and their applicability in the context of real-life engineering problems is discussed. A new approach based on an asymptotic approximation of multi-dimensional integrals is proposed. A closed-form expression for general order joint moments of arbitrary numbers of natural frequencies of linear stochastic systems is derived. The proposed method does not employ the ‘small randomness’ assumption usually used in perturbation based methods. Joint distributions of the natural frequencies are investigated using numerical examples and the results are compared with Monte Carlo simulation.
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Characteristics of Problems in Problem-based Learning
N. Sockalingam (Nachamma)
2010-01-01
textabstractThis thesis focuses on characteristics of problems in Problem-based Learning (PBL). Problems initiate the students’ learning process in PBL. Several studies have shown that the quality of problems has a positive influence on students’ academic achievement and interest. In addition, the q
Characteristics of Problems in Problem-based Learning
N. Sockalingam (Nachamma)
2010-01-01
textabstractThis thesis focuses on characteristics of problems in Problem-based Learning (PBL). Problems initiate the students’ learning process in PBL. Several studies have shown that the quality of problems has a positive influence on students’ academic achievement and interest. In addition, the
Obstacle problems in mathematical physics
Rodrigues, J-F
1987-01-01
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.
Institute of Scientific and Technical Information of China (English)
詹华税; 赵俊宁
2005-01-01
本文证明了拟线性退化抛物方程 (e)u/(e)t=n∑i=1 (e)/(e)xi(aij(u)(e)u/(e)xi)+n∑i=1 (e)bi(u)/(e)xi -c(u), u(x,0)=u0(x),aij(u)ξiξj≥0,(A)ξ∈Rn 的Cauchy问题BV解的唯一性和稳定性.
Analysis of the tracing problem
Institute of Scientific and Technical Information of China (English)
Nanfeng Jie; Hui Wang; YunqingSun
2005-01-01
Here the tracing problems are researched from two thoroughly different approaches: calculus method and numerical analysis. Generally speaking, the calculus method give a universal qualitative way to deal with such kind of problem, but the numerical analysis method can offer more further quantitative result for such kind of problem. Our research shows the detail results of application of these two methods in tracing problem.
Creating Games from Mathematical Problems
Pinter, Klara
2011-01-01
The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…
Dimensions of problem based learning
DEFF Research Database (Denmark)
Nielsen, Jørgen Lerche; Andreasen, Lars Birch
2013-01-01
The article contributes to the literature on problem based learning and problem-oriented project work, building on and reflecting the experiences of the authors through decades of work with problem-oriented project pedagogy. The article explores different dimensions of problem based learning...
Problem Order Implications for Learning
Li, Nan; Cohen, William W.; Koedinger, Kenneth R.
2013-01-01
The order of problems presented to students is an important variable that affects learning effectiveness. Previous studies have shown that solving problems in a blocked order, in which all problems of one type are completed before the student is switched to the next problem type, results in less effective performance than does solving the problems…
Extended Mixed Vector Equilibrium Problems
Directory of Open Access Journals (Sweden)
Mijanur Rahaman
2014-01-01
Full Text Available We study extended mixed vector equilibrium problems, namely, extended weak mixed vector equilibrium problem and extended strong mixed vector equilibrium problem in Hausdorff topological vector spaces. Using generalized KKM-Fan theorem (Ben-El-Mechaiekh et al.; 2005, some existence results for both problems are proved in noncompact domain.
DEFF Research Database (Denmark)
Dirckinck-Holmfeld, Lone; Balacheff, Nicolas; Bottino, Rosa Maria
2016-01-01
settings across Europe. However, to strengthen the various research practices and to develop a common scientific language on TEL research the Grand Challenge Problem is to establish a vivid network and a community of practice among the research labs. TELEARC (Technology Enhanced Learning European Advanced......Small and medium sized research labs (SMLs) are dominating European TEL research. This is justified by the great numbers of countries and regions in Europe needing to develop a research and innovation competence to facilitate the diverse educational systems contextualized in various institutional...... Research Consortium) has been established to realize such a network. The chapter presents the framework of TELEARC....
The Gilbert Arborescence Problem
Volz, M G; Ras, C J; Swanepoel, K J; Thomas, D A
2009-01-01
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characterise the local topological structure of Steiner points in MGAs, showing, in particular, that for a wide range of metrics and cost-functions the degree of each Steiner point is 3.
Elementary topology problem textbook
Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M
2008-01-01
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr
Respiratory problems in acromegaly.
Murrant, N J; Gatland, D J
1990-01-01
Death from respiratory causes in acromegaly is three times more common than in the general population and is most often the result of upper airways obstruction, although less commonly pulmonary dysfunction and disturbance of the central nervous system may occur. These factors may be found alone or in combination. Despite several reports of laryngeal involvement, upper airway obstruction in acromegaly is usually regarded as being due to macroglossia and pharyngeal soft tissue hypertrophy. We present four cases of acromegaly in which tracheostomy was required for laryngeal obstruction, with a review of the literature concerning the nature of respiratory problems in acromegaly.
1982-10-01
Artificial Intelig ~ence (Vol. III, edited by Paul R. Cohen and’ Edward A.. Feigenbaum)’, The chapter was written B’ Paul Cohen, with contributions... Artificial Intelligence (Vol. III, edited by Paul R. Cohen and EdWard A. Feigenbaum). The chapter was written by Paul R. Cohen, with contributions by Stephen...Wheevoats"EntermdI’ Planning and Problem ’Solving by Paul R. Cohen Chaptb-rXV-of Volumec III’of the Handbook of Artificial Intelligence edited by Paul R
Amiano, Mitch; Ethier, Kay; Thomas, Michael D
2006-01-01
Offering a unique approach to learning XML, this book walks readers through the process of building a complete, functional, end-to-end XML solutionFeatured case study is an online business product catalog that includes reports, data input/output, workflow, stylesheet formatting, RSS feeds, and integration with external services like Google, eBay, and AmazonThe format of presenting a problem and working through the design to come up with a solution enables readers to understand how XML markup allows a business to share data across applications internally or with partners or customers even thoug
Deser, S; Ong, Y C; Waldron, A
2014-01-01
The method of characteristics is a key tool for studying consistency of equations of motion; it allows issues such as predictability, maximal propagation speed, superluminality, unitarity and acausality to be addressed without requiring explicit solutions. We review this method and its application to massive gravity theories to show the limitations of these models' physical viability: Among their problems are loss of unique evolution, superluminal signals, matter coupling inconsistencies and micro-acausality (propagation of signals around local closed timelike/causal curves). We extend previous no-go results to the entire three-parameter range of massive gravity theories. It is also argued that bimetric models suffer a similar fate.
DEFF Research Database (Denmark)
Janstrup, Kira; Rose, Trine Høyer; Andersen, Kent Høj
The main purpose of this project is to use integer programming to create a model that minimizes the costs for container transportation by ship. To make the model as realistic as possible it will be based on information from a large shipping company about the vessel layout and container types....... In addition to our project two other projects are made where an optimal solution to the container stowage problem also is tried to be found, but by using constraint programming and local search instead respectively. We will therefore in the end compare these three methods and the achieved results on fastness...
DEFF Research Database (Denmark)
Janstrup, Kira
2010-01-01
The main purpose of this project is to use integer programming to create a model that minimizes the costs for container transportation by ship. To make the model as realistic as possible it will be based on information from a large shipping company about the vessel layout and container types....... In addition to our project two other projects are made where an optimal solution to the container stowage problem also is tried to be found, but by using constraint programming and local search instead respectively. We will therefore in the end compare these three methods and the achieved results on fastness...
Double pendulum contact problem
Directory of Open Access Journals (Sweden)
Špička J.
2014-06-01
Full Text Available The work concerns contact problems focused on biomechanical systems modelled by a multibody approach. The example is modelling of impact between a body and an infrastructure. The paper firstly presents algorithm for minimum distance calculation. An analytical approach using a tangential plain perpendicular to an initial one is applied. Contact force generated during impact is compared by three different continuous force models, namely the Hertz’s model, the spring-dashpot model and the non-linear damping model. In order to identify contact parameters of these particular models, the method of numerical optimization is used. Purpose of this method is to find the most corresponding results of numerical simulation to the original experiment. Numerical optimization principle is put upon a bouncing ball example for the purpose of evaluation of desirable contact force parameters. The contact modelling is applied to a double pendulum problem. The equation of motion of the double pendulum system is derived using Lagrange equation of the second kind with multipliers, respecting the contact phenomena. Applications in biomechanical research are hinted at arm gravity motion and a double pendulum impact example.
Some Undecidable Problems on Approximability of NP Optimization Problems
Institute of Scientific and Technical Information of China (English)
黄雄
1996-01-01
In this paper some undecidable problems on approximability of NP optimization problems are investigated.In particular,the following problems are all undecidable:(1) Given an NP optimization problem,is it approximable in polynomial time?(2)For any polynomial-time computable function r(n),given a polynomial time approximable NP optimization problem,has it a polynomial-time approximation algorithm with approximation performance ratio r(n) (r(n)-approximable)?(3)For any polynomial-time computable functions r(n),r'(n),where r'(n)
Math Forum @ Drexel, 2009
2009-01-01
Different techniques for understanding a problem can lead to ideas for never-used-before solutions. Good problem-solvers use a problem-solving strategy and may come back to it frequently while they are working on the problem to refine their strategy, see if they can find better solutions, or find other questions. Writing is an integral part of…
Abstraction and Problem Reformulation
Giunchiglia, Fausto
1992-01-01
In work done jointly with Toby Walsh, the author has provided a sound theoretical foundation to the process of reasoning with abstraction (GW90c, GWS9, GW9Ob, GW90a). The notion of abstraction formalized in this work can be informally described as: (property 1), the process of mapping a representation of a problem, called (following historical convention (Sac74)) the 'ground' representation, onto a new representation, called the 'abstract' representation, which, (property 2) helps deal with the problem in the original search space by preserving certain desirable properties and (property 3) is simpler to handle as it is constructed from the ground representation by "throwing away details". One desirable property preserved by an abstraction is provability; often there is a relationship between provability in the ground representation and provability in the abstract representation. Another can be deduction or, possibly inconsistency. By 'throwing away details' we usually mean that the problem is described in a language with a smaller search space (for instance a propositional language or a language without variables) in which formulae of the abstract representation are obtained from the formulae of the ground representation by the use of some terminating rewriting technique. Often we require that the use of abstraction results in more efficient .reasoning. However, it might simply increase the number of facts asserted (eg. by allowing, in practice, the exploration of deeper search spaces or by implementing some form of learning). Among all abstractions, three very important classes have been identified. They relate the set of facts provable in the ground space to those provable in the abstract space. We call: TI abstractions all those abstractions where the abstractions of all the provable facts of the ground space are provable in the abstract space; TD abstractions all those abstractions wllere the 'unabstractions' of all the provable facts of the abstract space are
The supersymmetric flavor problem
Dimopoulos, Savas K; Dimopoulos, Savas; Sutter, Dave
1995-01-01
The supersymmetric SU(3)\\times SU(2)\\times U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes \\mu \\rightarrow e + \\gamma and K^0 - \\bar{K}^0 mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for \\mu \\rightarrow e + \\gamma exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than M_{\\rm Planck}.
Routing and scheduling problems
DEFF Research Database (Denmark)
Reinhardt, Line Blander
be that the objects routed have an availability time window and a delivery time window or that locations on the path have a service time window. When routing moving transportation objects such as vehicles and vessels schedules are made in connection with the routing. Such schedules represent the time for the presence...... to a destination on a predefined network, the routing and scheduling of vessels in a liner shipping network given a demand forecast to be covered, the routing of manpower and vehicles transporting disabled passengers in an airport and the vehicle routing with time windows where one version studied includes edge...... of a connection between two locations. This could be an urban bus schedule where busses are routed and this routing creates a bus schedule which the passengers between locations use. In this thesis various routing and scheduling problems will be presented. The topics covered will be routing from an origin...
Edmondson, Amy C
2016-06-01
Companies today increasingly rely on teams that span many industries for radical innovation, especially to solve "wicked problems." So leaders have to understand how to promote collaboration when roles are uncertain, goals are shifting, expertise and organizational cultures are varied, and participants have clashing or even antagonistic perspectives. HBS professor Amy Edmondson has studied more than a dozen cross-industry innovation projects, among them the creation of a new city, a mango supply-chain transformation, and the design and construction of leading-edge buildings. She has identified the leadership practices that make successful cross-industry teams work: fostering an adaptable vision, promoting psychological safety, enabling knowledge sharing, and encouraging collaborative innovation. Though these practices are broadly familiar, their application within cross-industry teams calls for unique leadership approaches that combine flexibility, open-mindedness, humility, and fierce resolve.
Institute of Scientific and Technical Information of China (English)
G. Shanmugam
2015-01-01
The synonymous use of the general term“landslide”, with a built-in reference to a sliding motion, for all varieties of mass-transport deposits (MTD), which include slides, slumps, debrites, topples, creeps, debris avalanches etc. in subaerial, sublacustrine, sub-marine, and extraterrestrial environments has created a multitude of conceptual and nomen-clatural problems. In addition, concepts of triggers and long-runout mechanisms of mass movements are loosely applied without rigor. These problems have enormous implications for studies in process sedimentology, sequence stratigraphy, palaeogeography, petroleum geol-ogy, and engineering geology. Therefore, the objective of this critical review is to identify key problems and to provide conceptual clarity and possible solutions. Speciifc issues are the fol-lowing:(1) According to“limit equilibrium analyses”in soil mechanics, sediment failure with a sliding motion is initiated over a shear surface when the factor of safety for slope stability (F) is less than 1. However, the term landslide is not meaningful for debris lfows with a lfowing mo-tion. (2) Sliding motion can be measured in oriented core and outcrop, but such measurement is not practical on seismic proifles or radar images. (3) Although 79 MTD types exist in the geological and engineering literature, only slides, slumps, and debrites are viable depositional facies for interpreting ancient stratigraphic records. (4) The use of the term landslide for high-velocity debris avalanches is inappropriate because velocities of mass-transport processes cannot be determined in the rock record. (5) Of the 21 potential triggering mechanisms of sediment failures, frequent short-term events that last for only a few minutes to several hours or days (e.g., earthquakes, meteorite impacts, tsunamis, tropical cyclones, etc.) are more relevant in controlling deposition of deep-water sands than sporadic long-term events that last for thousands to millions of years (e
Instrumentation problems for physicians.
Turner, G O
1980-01-01
The physician has, for whatever reasons, diminished his or her level of involvement on the team dedicated to developing, refining, and evaluating medical technology. As a result, the challenge confronting the physician and the technology development team today is to orchestrate a team structure that will ensure the greatest input and commitment from physicians and other professionals during current and future technology development. The charges of cost escalation and dehumanization in our system of health care delivery will also be discussed, as will the lack of, or confusion about, access to data concerning cost of a given instrument, and fuzzy semantics and perspectives on technology and instrumentation. The author suggests answers to, or means to ameliorate, the problems.
Directory of Open Access Journals (Sweden)
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.
Baweja, R; Calhoun, S; Baweja, R; Singareddy, R
2013-10-01
Sleep complaints and sleep disorders are common during childhood and adolescence. The impact of not getting enough sleep may affect children's' physical health as well emotional, cognitive and social development. Insomnia, sleep-disordered breathing, parasomnias and sleep disturbances associated with medical and psychiatric disorders are some of the commonly encountered sleep disorders in this age group. Changes in sleep architecture and the amount of sleep requirement associated with each stage of development should be considered during an evaluation of sleep disorders in children. Behavioral treatments should be used initially wherever possible especially considering that most pharmacologic agents used to treat pediatric sleep disorders are off-label. In this review we address the most common sleep problems in children/adolescents as they relate to prevalence, presentation and symptoms, evaluation and management.
Energy Technology Data Exchange (ETDEWEB)
Walkup, Elizabeth [Stanford Univ., CA (United States)
2016-06-01
Passwords are an ubiquitous, established part of the Internet today, but they are also a huge security headache. Single sign-on, OAuth, and password managers are some of the solutions to this problem. OAuth is a new, popular method that allows people to use large, common authentication providers for many web applications. However, it comes at the expense of some privacy: OAuth makes users easy to track across websites, applications, and devices. Password managers put the power in the hands of the users, but this vulnerability survey reveals that you have to be extremely careful which program you choose. All in all, password managers are the solution of choice for home users and small organizations, but large companies will probably want to invest in their own SSO solutions.
Benson, Brian
2007-01-01
In this paper we study the Three Hat Problem which appeared in Puzzle Corner of the Technology Review magazine. This puzzle gives a scenario in which three players wearing hats are sitting together and each hat can be seen by everyone except the player that is wearing that hat. Each player is told that all of the hats contain a positive integer and that two of the integers add to the third. In an ordered, turn-wise, modular fashion, each player truthfully states whether or not he knows his integer. We give a strategy which allows for one of the players to solve for his integer for all possible integer configurations of the puzzle and prove it is the optimal such strategy.
Gaussian quantum marginal problem
Eisert, J; Sanders, B C; Tyc, T
2007-01-01
The quantum marginal problem asks what local spectra are consistent with a given state of a composite quantum system. This setting, also referred to as the question of the compatibility of local spectra, has several applications in quantum information theory. Here, we introduce the analogue of this statement for Gaussian states for any number of modes, and solve it in generality, for pure and mixed states, both concerning necessary and sufficient conditions. Formally, our result can be viewed as an analogue of the Sing-Thompson Theorem (respectively Horn's Lemma), characterizing the relationship between main diagonal elements and singular values of a complex matrix: We find necessary and sufficient conditions for vectors (d1, ..., dn) and (c1, ..., cn) to be the symplectic eigenvalues and symplectic main diagonal elements of a strictly positive real matrix, respectively. More physically speaking, this result determines what local temperatures or entropies are consistent with a pure or mixed Gaussian state of ...
Muna, Demitri; Allen, Alice; Ashley, Richard; Asmus, Daniel; Azzollini, Ruyman; Bannister, Michele; Beaton, Rachael; Benson, Andrew; Berriman, G Bruce; Bilicki, Maciej; Boyce, Peter; Bridge, Joanna; Cami, Jan; Cangi, Eryn; Chen, Xian; Christiny, Nicholas; Clark, Christopher; Collins, Michelle; Comparat, Johan; Cook, Neil; Croton, Darren; Davids, Isak Delberth; Depagne, Éric; Donor, John; Santos, Leonardo A dos; Douglas, Stephanie; Du, Alan; Durbin, Meredith; Erb, Dawn; Faes, Daniel; Fernández-Trincado, J G; Foley, Anthony; Fotopoulou, Sotiria; Frimann, Søren; Frinchaboy, Peter; Garcia-Dias, Rafael; Gawryszczak, Artur; George, Elizabeth; Gonzalez, Sebastian; Gordon, Karl; Gorgone, Nicholas; Gosmeyer, Catherine; Grasha, Katie; Greenfield, Perry; Grellmann, Rebekka; Guillochon, James; Gurwell, Mark; Haas, Marcel; Hagen, Alex; Haggard, Daryl; Haines, Tim; Hall, Patrick; Hellwing, Wojciech; Herenz, Edmund Christian; Hinton, Samuel; Hlozek, Renee; Hoffman, John; Holman, Derek; Holwerda, Benne Willem; Horton, Anthony; Hummels, Cameron; Jacobs, Daniel; Jensen, Jens Juel; Jones, David; Karick, Arna; Kelley, Luke; Kenworthy, Matthew; Kitchener, Ben; Klaes, Dominik; Kohn, Saul; Konorski, Piotr; Krawczyk, Coleman; Kuehn, Kyler; Kuutma, Teet; Lam, Michael T; Lane, Richard; Liske, Jochen; Lopez-Camara, Diego; Mack, Katherine; Mangham, Sam; Mao, Qingqing; Marsh, David J E; Mateu, Cecilia; Maurin, Loïc; McCormac, James; Momcheva, Ivelina; Monteiro, Hektor; Mueller, Michael; Munoz, Roberto; Naidu, Rohan; Nelson, Nicholas; Nitschelm, Christian; North, Chris; Nunez-Iglesias, Juan; Ogaz, Sara; Owen, Russell; Parejko, John; Patrício, Vera; Pepper, Joshua; Perrin, Marshall; Pickering, Timothy; Piscionere, Jennifer; Pogge, Richard; Poleski, Radek; Pourtsidou, Alkistis; Price-Whelan, Adrian M; Rawls, Meredith L; Read, Shaun; Rees, Glen; Rein, Hanno; Rice, Thomas; Riemer-Sørensen, Signe; Rusomarov, Naum; Sanchez, Sebastian F; Santander-García, Miguel; Sarid, Gal; Schoenell, William; Scholz, Aleks; Schuhmann, Robert L; Schuster, William; Scicluna, Peter; Seidel, Marja; Shao, Lijing; Sharma, Pranav; Shulevski, Aleksandar; Shupe, David; Sifón, Cristóbal; Simmons, Brooke; Sinha, Manodeep; Skillen, Ian; Soergel, Bjoern; Spriggs, Thomas; Srinivasan, Sundar; Stevens, Abigail; Streicher, Ole; Suchyta, Eric; Tan, Joshua; Telford, O Grace; Thomas, Romain; Tonini, Chiara; Tremblay, Grant; Tuttle, Sarah; Urrutia, Tanya; Vaughan, Sam; Verdugo, Miguel; Wagner, Alexander; Walawender, Josh; Wetzel, Andrew; Willett, Kyle; Williams, Peter K G; Yang, Guang; Zhu, Guangtun; Zonca, Andrea
2016-01-01
The Astropy Project (http://astropy.org) is, in its own words, "a community effort to develop a single core package for Astronomy in Python and foster interoperability between Python astronomy packages." For five years this project has been managed, written, and operated as a grassroots, self-organized, almost entirely volunteer effort while the software is used by the majority of the astronomical community. Despite this, the project has always been and remains to this day effectively unfunded. Further, contributors receive little or no formal recognition for creating and supporting what is now critical software. This paper explores the problem in detail, outlines possible solutions to correct this, and presents a few suggestions on how to address the sustainability of general purpose astronomical software.
Directory of Open Access Journals (Sweden)
Erik af Edholm
1975-01-01
Full Text Available The myth of the recurrence of the golden age after a period of accelerating miseries ("messianic woes" in the near future is of course not peculiar to the chiliasm of the European later middle ages. On the contrary, it belongs to the basic eschatological themes of millenarism in general. These themes are found also in Hindu tradition. To determine those general characteristics of traditional Hindu society which can contribute to an explanation of the relative unimportance of peasant rebellions and the lack of chiliastic mass movements, is not a problem to be solved within the field of the history of religions. For example, the egalitarian message of the bhakti saints, disputing the hierarchy, did not preclude that the salvationist sects did adapt to the caste system. The religious movements contributed to and gave ideological form to adjustments within the existing social structure. Obviously there was little need for millenarism in this process.
Mauroy, Alexandre; Taslakian, Perouz; Langerman, Stefan; Jungers, Raphaël
2016-09-01
A four-bar linkage is a mechanism consisting of four rigid bars which are joined by their endpoints in a polygonal chain and which can rotate freely at the joints (or vertices). We assume that the linkage lies in the 2-dimensional plane so that one of the bars is held horizontally fixed. In this paper we consider the problem of reconfiguring a four-bar linkage using an operation called a pop. Given a four-bar linkage, a pop reflects a vertex across the line defined by its two adjacent vertices along the polygonal chain. Our main result shows that for certain conditions on the lengths of the bars, the neighborhood of any configuration that can be reached by smooth motion can also be reached by pops. The proof relies on the fact that pops are described by a map on the circle with an irrational number of rotation.
Energy Technology Data Exchange (ETDEWEB)
Angelier, J.P.
1982-11-01
Ecuador used to be referred to as a typical ''banana republic'', but beginning in 1973, it became South America's second biggest oil exporter and during that same year it was admitted into the Organization of Petroleum Exporting Countries. Ecuador then established a nationalistic policy which succeeded in giving it a certain measure of control over its oil industry even if serious problems are still hindering the management of this industry. Today, Ecuador is facing an alternative: either it continues along the road it traced beginning in 1973, or else it takes a road which aims at relatively autonomous development of the national economy, or else it becomes a country which essentially lives from its oil revenues, produced and exploited by others.
Problem Teologis Ideologi Komunisme
Directory of Open Access Journals (Sweden)
Muhamad Yakub Mubaro
2017-05-01
Full Text Available It is known that the communism had affected the history of this world. This ideology had succeeded influencing a third of the world in less than one century after Karl Marx’s death and it had caused some revolutionary movements at some countries of the world. It is interesting to say that even what Marx had predicted about the history of human being in the future was not surely proven, but his ideas have been affecting people. But, the communism has serious problems related to the theological matter for sure. It could make people becoming atheist. Moreover, it could create the people hate their religion, but they could become religion’s antagonists. Marx’s hatred toward religions was expressed by the words: “Religion is the opium of the masses”. Then Lenin, another figure of the communism, did a discrimination to religious people, as well as, Joseph Stalin and Mao Zedong who prohibited all kinds of religious activities during their lifetime. Long time ago, thousands of Indonesian Moslems were becoming victims of a communist party in Indonesia (PKI. Nowadays, the communism doctrine begins to appear and affect some youths of Indonesia. Perhaps, it does because they have been frustrated and being disappointed by the socio-political condition which is controlled by modern capitalists. But, they have to be aware that the communism is not a solution. In fact, it is surely dangerous. It could ruin religions’ concepts. Hence, this article would try to explain some theological problems of the communism ideology.
Institute of Scientific and Technical Information of China (English)
ZENG; Jiwen(
2001-01-01
［1］Brauer, R., Representations of finite groups, in Lectures in Mathematics, Vol. 1, New York: Wiley, 1963, 133－175.［2］Feit, W. , The Representation Theory of Finite Groups, Amsterdam: North-Holland, 1982.［3］Külshammer, B., Landau's theorem for p-blocks of p-solvable groups, J. Reine Angew. Math., 1990, 404: 189－191.［4］Külshammer B., Robinson, G. R., Alperin-Mckey implies Brauer's problem 21, J. Algebra, 1996, 180: 208－210.［5］Zeng Jiwen, An inequality of block invariants, J. Algebra, 1997, 193: 724－727.［6］Nagao, N., Tsushima, Y., Representations of Finite Groups, New York: Academic Press, Inc., 1989.［7］Robinson, G. R., On Brauer's k(B) problem, J. Algebra, 1992, 147: 450－455.［8］Zhang Jiping, p-regular orbits and p-blocks of defect zero, Comm. Algebra, 1993, 21(1): 299－307.［9］Xu Minyao, Huang ,Jianhua, An Introduction to Finite Groups (in Chinese), Vol. 2, Beijing: Science Press, 1999.［10］Alperin, ,J. L. , Weights for finite group, Proc. Sympos. Pure Math. , 1987, 47: 369－379.［11］Puig, L., Usami, Y., Perfect isometrics for blocks with Abelian defect groups and cyclic four inertial quotients, J. Algebra,1996.［12］Dade, E. C., Counting characters in blocks, I, Invent. Math., 1992, 109: 187－210.
Fostering Information Problem Solving Skills Through Completion Problems and Prompts
Frerejean, Jimmy; Brand-Gruwel, Saskia; Kirschner, Paul A.
2012-01-01
Frerejean, J., Brand-Gruwel, S., & Kirschner, P. A. (2012, September). Fostering Information Problem Solving Skills Through Completion Problems and Prompts. Poster presented at the EARLI SIG 6 & 7 "Instructional Design" and "Learning and Instruction with Computers", Bari, Italy.
Fostering information problem solving skills through completion problems and prompts
Frerejean, Jimmy; Brand-Gruwel, Saskia; Kirschner, Paul A.
2012-01-01
Frerejean, J., Brand-Gruwel, S., & Kirschner, P. A. (2012, November). Fostering information problem solving skills through completion problems and prompts. Poster presented at the ICO Fall School 2012, Girona, Spain.
Mechanics problems in undergraduate physics
Strelkov, S P
2013-01-01
Problems in Undergraduate Physics, Volume I: Mechanics focuses on solutions to problems in physics. The book first discusses the fundamental problems in physics. Topics include laws of conservation of momentum and energy; dynamics of a point particle in circular motion; dynamics of a rotating rigid body; hydrostatics and aerostatics; and acoustics. The text also offers information on solutions to problems in physics. Answers to problems in kinematics, statics, gravity, elastic deformations, vibrations, and hydrostatics and aerostatics are discussed. Solutions to problems related to the laws of
Problem effectiveness in a course using problem-based learning
D.H.J.M. Dolmans (Diana); W.H. Gijselaers (Wim); H.G. Schmidt (Henk); S.B. van der Meer
1993-01-01
textabstractBackground. Problem-based learning (PBL) emphasizes active generation of learning issues by students. Both students and reachers, however, tend to worry that not all important knowledge will be acquired. To explore this question, problem effectiveness (i.e., for each problem, the degree
Problem Solving through an Optimization Problem in Geometry
Poon, Kin Keung; Wong, Hang-Chi
2011-01-01
This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…
Problem based learning: Cognitive and metacognitive processes during problem analysis
W.S. de Grave; H.P.A. Boshuizen (Henny); H.G. Schmidt (Henk)
1996-01-01
textabstractAn important phase of problem-based learning in a tutorial group is problem analysis. This article describes a study investigating the ongoing cognitive and metacognitive processes during problem analysis, by analysing the verbal communication among group members, and their thinking proc
Problem effectiveness in a course using problem-based learning
D.H.J.M. Dolmans (Diana); W.H. Gijselaers (Wim); H.G. Schmidt (Henk); S.B. van der Meer
1993-01-01
textabstractBackground. Problem-based learning (PBL) emphasizes active generation of learning issues by students. Both students and reachers, however, tend to worry that not all important knowledge will be acquired. To explore this question, problem effectiveness (i.e., for each problem, the degree
Problem based learning: Cognitive and metacognitive processes during problem analysis
W.S. de Grave; H.P.A. Boshuizen (Henny); H.G. Schmidt (Henk)
1996-01-01
textabstractAn important phase of problem-based learning in a tutorial group is problem analysis. This article describes a study investigating the ongoing cognitive and metacognitive processes during problem analysis, by analysing the verbal communication among group members, and their thinking
Feder, Tomás
2009-06-01
Results on graph turnpike problem without distinctness, including its NP-completeness, and an O(m+n log n) algorithm, is presented. The usual turnpike problem has all pairwise distances given, but does not specify which pair of vertices w e corresponds to. There are two other problems that can be viewed as special cases of the graph turnpike problem, including the bandwidth problem and the low-distortion graph embedding problem. The aim for the turnpike problem in the NP-complete is to orient the edges with weights w i in either direction so that when the whole cycle is transversed in the real line, it returns to a chosen starting point for the cycle. An instance of the turnpike problem with or without distinctness is uniquely mappable if there exists at most one solution up to translation and choice of orientation.
ON VECTOR NETWORK EQUILIBRIUM PROBLEMS
Institute of Scientific and Technical Information of China (English)
Guangya CHEN
2005-01-01
In this paper we define a concept of weak equilibrium for vector network equilibrium problems.We obtain sufficient conditions of weak equilibrium points and establish relation with vector network equilibrium problems and vector variational inequalities.
Duality in constrained location problems
DEFF Research Database (Denmark)
Juel, Henrik; Love, Robert F.
1987-01-01
The dual of a facility location problem with general norms, distance constraints, and linear constraints is formulated.......The dual of a facility location problem with general norms, distance constraints, and linear constraints is formulated....
Duality in constrained location problems
DEFF Research Database (Denmark)
Juel, Henrik; Love, Robert F.
1987-01-01
The dual of a facility location problem with general norms, distance constraints, and linear constraints is formulated.......The dual of a facility location problem with general norms, distance constraints, and linear constraints is formulated....
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Dementia - behavior and sleep problems
... this page: //medlineplus.gov/ency/patientinstructions/000029.htm Dementia - behavior and sleep problems To use the sharing ... on this page, please enable JavaScript. People with dementia , often have certain problems when it gets dark ...
Sherlock Holmes, Master Problem Solver.
Ballew, Hunter
1994-01-01
Shows the connections between Sherlock Holmes's investigative methods and mathematical problem solving, including observations, characteristics of the problem solver, importance of data, questioning the obvious, learning from experience, learning from errors, and indirect proof. (MKR)
Direct Problems and Inverse Problems in Biometric Systems
Directory of Open Access Journals (Sweden)
Mihailescu Marius Iulian
2013-10-01
Full Text Available The article purpose is to describe the two sides of biometrics technologies, direct problems and inverse problems. The advance that we face today in field of Information Technology makes Information Security an inseparable part. The authentication has a huge role when we deal about security. The problems that can appear in implementing and developing biometrics systems is raising many problems, and one of the goal of this article is to focus on direct and inverse problems which is a new and challenging branch in biometrics technologies.