bluuebunny/crossref_metadata_2025 huggingface dataset:
Newton iterations without inverting the Derivative
Authors: Scheurle J. , Kirchgässner K.
Published: March 2007

We describe an iteration procedure in a Banach space which is quadratically convergent like Newton's method. In fact, it is a modification of the latter. The inverted derivatives are replaced by so‐called contractors which are constructed recursively. Moreover, this method is extended to a scale of Banach spaces. It turns out that the rate of convergence remains quadratic, even if the norms of the contractors are increasing exponentially. A hard implicit function theorem results. In particular, this theorem can be applied to prove existence of quasiperiodic solutions for the Lorenz model of stationary convection.
A local compactness theorem for Maxwell's equations
Authors: Weber Ch. , Werner P.
Published: March 2007

The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor‐valued function on G satisfying certain restrictions, and let {n} be a sequence of vector‐valued functions on G where the L2‐norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2‐convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ϵ or as magnetic permeability μ, respectively.

These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.
Gradient bounds for plasma confinement
Authors: Stakgold I. , Hsiao G. C.
Published: March 2007

The problem of plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one‐dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attained.
Differentiable dependence upon the data in a one‐phase Stefan problem
Authors: Jochum P. , Brosowski B.
Published: March 2007

It is well known that the free boundary of the one‐phase Stefan problem (1.1–5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.
Über die Radon‐Transformation kreissymmetrischer Funktionen und ihre Beziehung zur Sommerfeldschen Theorie der Hankelfunktionen
Authors: Müller C. , Richberg R. , Leis R.
Published: March 2007

For the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer‐feld's integral for H, yielding a representation of products which generalizes Nicholson's integral for |H| 2.
Numerical solution of Hopf bifurcation problems
Authors: Weber H. , Törnig W.
Published: March 2007

We present two numerical methods for the solution of Hopf bifurcation problems involving ordinary differential equations. The first one consists in a discretization of the continuous problem by means of shooting or multiple shooting methods. Thus a finite‐dimensional bifurcation problem of special structure is obtained. It may be treated by appropriate iterative algorithms. The second approach transforms the Hopf bifurcation problem into a regular nonlinear boundary value problem of higher dimension which depends on a perturbation parameter ϵ. It has isolated solutions in the ϵ‐domain of interest, so that conventional discretization methods can be applied. We also consider a concrete Hopf bifurcation problem, a biological feedback inhibition control system. Both methods are applied to it successfully.
Zur L∞‐Konvergenz finiter Elemente bei parabolischen Differentialgleichungen
Authors: Dobrowolski M. , Leis R.
Published: March 2007

For a parabolic model problem it is shown that the convergence rate of higher order finite element approximation is quasioptimal in L∞. Moreover, the estimate does not depend on the interval [0, T]. The essential tool of the proof is a modified weighted norm technique.
Eigenvalue bounds for Hill's equation
Authors: Lortz D. , Rebhan E. , Törnig W.
Published: March 2007

For Hill's equation

equation image

the lowest eigenvalue a0 of the boundary value problem y(x + 1) = y(x) is considered. Introducing Lp norms of the function f(x), lower bounds for a0 which depend only on this norm are derived for p = 1,2 and ∞ by solving a variational principle. For these lower bounds analytical expressions are obtained. The quality of the approximations thus obtained is discussed for Mathieu's equation and an application in magnetohydrodynamics is considered.
Galerkin's method and stability
Authors: Jones D. S.
Published: March 2007

Approximation in least squares by Galerkin's method leads to a consideration of strongly minimal systems. Theorems are derived which permit the recognition of systems which are not strongly minimal from the characteristics of the elements themselves. Normalised systems cannot be strongly minimal without their eigenvalues being bounded above.

Speared systems, which have desirable properties, are introduced and their main features determined. Convergence earmarks and error bounds are exposed.

A new definition of stability, which is self‐checking in a computation, is suggested and its attributes delineated.

The extension of the theory to equations involving positive‐definite operators is mentioned.
Über die Gaußsche Methode zur angenäherten Berechnung von Integralen
Authors: Freeden W. , Leis R.
Published: March 2007

The purpose of this paper is the application of Green's theory and Green‐Lagrange integral formulas relative to Legendre's differential operator to obtain integral expressions of remainder terms in Gaussian mechanical quadratures.
Ein Existenzsatz für die Vlasov‐Gleichung mit selbstkonsistentem Magnetfeld
Authors: Neunzert H. , Petry K. H.
Published: March 2007

The Vlasov equation with electric and magnetic fields generated by the distribution of the plasma is considered. For a simplified model with one space and two velocity coordinates and a mollification of the spatial density and the mean velocity in the Maxwell equations an existence and uniqueness theorem is proved.
Some remarks on the horizontal line method
Authors: Picard R. , Leis R.
Published: March 2007

In the following paper a methodological survey with respect to applications of the horizontal line method (Rothe's method) to a class of initial boundary value problems is given. By means of results from abstract perturbation theory, convergence results and error estimates are established for several special initial boundary value problems of mathematical physics.
Monoton einschließend konvergente iterationsprozesse vom gauß‐seidel‐typ zur lösung nichtlinearer gleichungssysteme im RN und anwendungen
Authors: Törnig W.
Published: March 2007

In this paper we describe a class of Gauß‐Seidel iterations for the solution of large sparse nonlinear systems of equations. For suitable starting vectors every method of this class is monotonically convergent with respect to both sides. The result will be applied to the numerical solution of nonlinear boundary‐value problems and boundary layer problems.
High Hartmann number flow through a rectangular duct with unequally and finitely conducting walls
Authors: Chee‐Seng Lim , Eckhaus W.
Published: March 2007

Nonsymmetric Hartmann flow through a rectangular duct is investigated for thin duct walls with, generally, unequal but finite conductivities. A high Hartmann number is adopted. Consistent with known phenomena, both Hartmann layers transverse to the applied magnetic field are assumed to be separated from the two side boundary layers by four corner regions plus four inner corner regions. The method of singular perturbations and matched asymptotic expansions is applied to the coupled system. The equations governing the core and Hartmann layers are first partially resolved for leading terms. This is then followed by tackling equations governing one side layer and two adjacent corner regions. The latters' incorporation secures, for the former, only those boundary conditions that are compatible along the transverse walls. Both corner regions are denied access to non‐required boundary conditions along the neighbouring side wall by the adjoining inner corner regions. However, the latters' boundary value problems need not be tackled for the acquirement of only dominant terms beyond all four inner corner regions. The complementary side layer and associated corners are accounted for by a non‐symmetric reflection principle.

Results reveal that a difference between conductivities in the transverse walls together with at least one finitely conducting side wall impart to disturbances within the core and Hartmann layers (i) a nontrivial dependence on the transverse coordinate relative to the magnetic field and flow in addition to the (usual) dependence on the field aligned coordinate,
(ii) a dependence on side wall parameters in addition to the dependence on transverse wall parameters.

Applications to related situations are considered. These include the case for a perfectly conducting lower wall, a finitely conducting upper wall, and equally and finitely conducting side walls.
Efficient implementation of ‘Optimal’ algorithms in computerized tomography
Authors: Natterer F. , Hadeler K. P.
Published: March 2007

We describe three optimal algorithms for the reconstruction of a function in R2 from a finite number of line or strip integrals: Optimal recovery, Bayes estimate, Tikhonov‐Phillips method. In the case of a rotationally invariant scanning geometry we show that the resulting linear system is a block‐cyclic convolution. This observation leads to algorithms which are roughly as efficient as filtered backprojection which is one of the standard methods. The algorithms can be applied to the case of hollow and truncated projections. Numerical examples are given.
Bifurcation results for a class of periodic quasi‐linear parabolic equations
Authors: de Mottoni P. , Schiaffino A. , Hadeler K. P.
Published: March 2007

We consider the problem where a and f are 1‐periodic in t, a is positive, f satisfies appropriate decreasing conditions; smoothness of a, f, ∂Ω is also assumed. Denote by λ0 the principal eigenvalue of Δ with zero Dirichlet boundary conditions, and define . We prove: (a) if ε ≤ 0, then no non‐negative periodic solution exists but zero, and any solution with continuous non‐negative initial datum converges to zero uniformly as t → ∞; (b) if ε > 0, then a unique non trivial non‐negative 1‐periodic solution u* exists, and any solution with continuous, non‐negative not identically zero initial datum approaches uniformly u* as t → ∞.
Asymptotic relationship between telegraphic and diffusion equations
Authors: Mika J. , Stankiewicz R. , Neunzert H.
Published: March 2007

In the paper it is considered the generalized telegraphic equation represented by the system of four evolution equations, containing a small positive parameter multiplying some of the time derivatives. It is shown that if the small parameter tends to zero, the solution to the telegraphic equation tends asymptotically to the solution of the diffusion equation obtained from the former one by putting the small parameter equal to zero.
Free boundary problems for the laplace equation: A priori estimates, existence theorems, asymptotic behaviours
Authors: Dervieux A. , Kawarada H. , Fujita H.
Published: March 2007

This work is devoted to Free Boundary Problems with Laplace equation Δu = f in the domain and the two conditions on the Free Boundary u = 1 and |grad u| = λ = const. In the model problems which we study, three cases arise: 1) f = 0, λ is given, 2) f = 0, λ is unknown and the length of the Free Boundary is given, 3) f ≠ 0, λ = 0 (Obstacle Problem).
Sur une Interprétation Mathématique de l'Intégrale de Rice en Théorie de la Rupture Fragile
Authors: Destuynder P. , Djaoua Palaiseau Et M. , Chesnay Le , Nedelec J. C.
Published: March 2007

We formulate the assumptions under which Rice J integral and the critical energy release rate, which occur in fragile fracture mechanic, are equivalent.
Irregular multipoint eigenvalue problems
Authors: Freiling G. , Neunzert H.
Published: March 2007

We prove asymptotic estimates for the Green's function of irregular multipoint eigenvalue problems, these estimates are fundamental for the expansion of functions into a series of eigenfunctions of irregular eigenvalue problems.
A constructive approximation theorem for the oblique derivative problem in potential theory
Authors: Freeden W. , Kersten H. , Leis R.
Published: March 2007

The (exterior) oblique derivative problem of potential theory magnified image is considered where l is a C(1,λ)‐vector field on a regular boundary ∂Ge in Euclidean space R3 and the direction l at any point of ∂Ge forms with the outside normal n an angle ∢ (l, n) satisfying cos ∢ (l, n) ≥ c > 0. An approximation of the uniquely determined solution is given by use of trial functions {Φn}n=0,1,… harmonic in some region containing Ge and suitable for numerical purpose (for instance: solid spherical harmonics, certain sequences of fundamental solutions). The system {l▽Φn+hΦn}n=0,1,… defined on ∂Ge is shown to be closed and complete in the pre‐Hilbert space C(0,λ)(∂Ge) of λ‐Hölder continuous functions.
The decay of solutions of the Carleman model
Authors: Illner R. , Reed M. C. , Neunzert H.
Published: March 2007

We prove that for positive initial data u0, v0 ϵ C1 (R) ∩ L1 (R) vanishing at infinity, the solution u(x, t) v(x, t) of the Carleman model satisfies the estimate The constant C depends only on the initial mass m.
Scattering techniques for a one dimensional inverse problem in geophysics
Authors: Carroll R. , Santosa F. , Paynec L.
Published: March 2007

A one dimensional problem for SH waves in an elastic medium is treated which can be written as vtt = A−1 (Avy)y, A = (ϱμ)1/2, ϱ = density, and μ = shear modulus. Assume A ϵ C1 and A′/A ϵ L1; from an input vy(t, 0) = ∂(t) let the response v(t, 0) = g(t) be measured (v(t, y) = 0 for t < 0). Inverse scattering techniques are generalized to recover A(y) for y > 0 in terms of the solution K of a Gelfand‐Levitan type equation, .
New asymptotic expansion algorithm for singularly perturbed evolution equations
Authors: Mika J. , Eckhaus W.
Published: March 2007

A new asymptotic expansion algorithm related to the Chapman‐Enskog expansion in kinetic theory is applied to systems of linear evolution equations. The uniform convergence of the asymptotic solution to the exact one is shown. The algorithm is applied to the linearized Carleman model of the Boltzmann equation, to the neutron transport equation, and to the Fokker‐Planck equation.
Randwertaufgaben in der verallgemeinerten Potentialtheorie
Authors: Picard R. , Leis R.
Published: March 2007

The Neumann and Dirichlet boundary value problem of generalized potential theory is considered. Based on a compact imbedding result, existence and uniqueness theorems are obtained for Riemannian manifolds with compact boundary (‘interior and exterior domains’).
A singular perturbation problem for linear operators with an application to electrostatic and magnetostatic boundary and transmission problems
Authors: Engl H. W. , Kress R. , Meister E.
Published: March 2007

The treatment of certain electro‐ and magnetostatic boundary and transmission problems by boundary integral equations leads to parameter‐dependent integral equations of the second kind. The integral operators involved have the property that the dimension of their nullspaces changes between two nonzero values (depending on the geometry of the problem) as the parameter tends to zero. We investigate the continuous dependence of solutions to these equations on the parameter. To this end, we treat the problem of continuous dependence of solutions to parameter‐dependent linear operator equations of the second kind in a Banach space in the framework of generalized inverses.
Study of motions of a vibrating string subject to solid friction
Authors: Cabannes H. , Neunzert H.
Published: March 2007

In this paper we consider a string moving in its plane and subject to solid friction (Coulomb's law). It is known that when the time increases indefinitely the string reaches an equilibrium position and by analogy with the case of a mass point we ask if the equilibrium is reached after a finite time. We prove that this is the case when the string is initially at rest and 1. when the initial shape possesses a second derivative bounded by certain limits, or 2. when the initial shape is formed by two straight line segments. In the last section we obtain some partial results when the string is initially at rest in the shape of a polygonal line. The case of an arbitrary initial position is still an open problem.
Bifurcation of periodic orbits in coupled chemical reactors I
Authors: Kirchgraber U. , Hagedorn P.
Published: March 2007

This paper provides a rigorous approach to the problem of bifurcation of periodic orbits of a chemical reactor system recently studied by Marek and Stuckl, and by Neu. Using transformation techniques and invariant manifold theory the problem is reduced to a two‐parameter bifurcation equation in R.
Über das asymptotische Verhalten thermoelastischer Wellen im R3
Authors: Leis R.
Published: March 2007

In [L] the author provided existence theorems for initial‐boundary‐value problems in thermoelasticity for unbounded domains. Continuing this work the asymptotic behaviour of solutions in R3 with respect to t → ∞ will be described in this paper.
Finite element approximation of vector fields given by curl and divergence
Authors: Neittaanmäki P. , Saranen J. , Mitchell A. R.
Published: March 2007

In this paper a finite element approximation scheme for the system curl is considered. The use of pointwise approximation of the boundary condition leads to a nonconforming method. The error estimate is proved and numerically tested.
Mathematische Behandlung ernes Modells der Haemodialyse
Authors: Klingelhöfer D. , Koch G. F. , Krabs W. , Hadeler K. P.
Published: March 2007

In this paper a simple mathematical model for the process of hemodialysis is presented. This model is based on a system of two linear differential equations of first order with partly discontinuous coefficients that describe the time‐development of the concentrations of a certain toxin (like urea) in the intra‐ and extracellular part of the human body. The main result is the existence of periodic positive solutions of this system under the natural assumption that the generation of the toxin and its removal by hemodialysis are periodic processes. These periodic positive solutions are also computed numerically for a realistic choice of the coefficients of the modelling differential equations.
On the Vlasov hierarchy
Authors: Spohn H. , Neunzert H.
Published: March 2007

Motivated by a recent paper of H. Narnhofer and G. Sewell, we investigate the problem of existence and uniqueness of solutions of the Vlasov hierarchy. It is shown that the unique solution of the Vlasow hierarchy is induced by the flow on the space of probability measures on R6 which is obtained from the solution of the Vlasov equation.
The impedance boundary value problem for the time harmonic Maxwell equations
Authors: Colton D. , Kress R. , Hsiao G. C.
Published: March 2007

The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem.
Approximation of the scattering state by means of the radiation boundary condition
Authors: Kako T. , Fujita H.
Published: March 2007

The approximation sequence for the scattering state is constructed by the solutions for the reduced wave equations in some bounded domains with radiation conditions at their boundary. The corresponding discrete approximation is also considered by the Bubnov‐Galerkin method.
Regularity theorems for Maxwell's equations
Authors: Weber C. , Werner P.
Published: March 2007

Methods using the theory of distributions and Hilbert space operators have been very powerful in the past to achieve uniqueness and existence results for Maxwell's equations. In this paper conditions are given when such abstract “Hilbert space”‐solutions represent differentiable “regular” functions which satisfy Maxwell's equations, boundary conditions, and transmission conditions in the classical sense.
Einige singuläre Integralgleichungen in der Relaxationsgasdynamik
Authors: Schilling H. , Meister E.
Published: March 2007

The relaxation drag of a slender profile or profile arrangement in plane, steady, relaxing subsonic gas flow is studied. Especially, the question is discussed which shapes the profiles must have in order to minimize the relaxation drag. These optimization problems lead to a number of singular integral equations of first kind, one of which is solved as an example with the help of a suitable chosen ansatz.
On spherical spline interpolation and approximation
Authors: Freeden W. , Törnig W.
Published: March 2007

Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace‐)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used to interpolate data discretely given on the sphere. A method is presented that allows the smoothing of irregularities in measured values or experimental data. Extensions of Peano's theorem and Sard's theory of best approximation to the spherical case are given by integral formulas. Schoenberg's theorem is transcribed into spherical nomenclature.
Local solvability of a nonstationary leakage problem for an ideal incompressible fluid, 3
Authors: Zajaczkowski W. M. , Piskorek A.
Published: March 2007

In this paper we prove the existence and uniqueness of solutions of the leakage problem for the Euler equations in bounded domain Ω C R3 with corners π/n, n = 2, 3… We consider the case where the tangent components of the vorticity vector are given on the part S1 of the boundary where the fluid enters the domain. We prove the existence of an unique solution in the Sobolev space Wpl(Ω), for arbitrary natural l and p > 1. The proof is divided on three parts: (1) the existence of solutions of the elliptic problem in the domain with corners

where v – velocity vector, ω – vorticity vector and n is an unit outward vector normal to the boundary,
(2) the existence of solutions of the following evolution problem for given velocity vector

(3) the method of successive approximations, using solvability of problems (1) and (2).
On the decay of symmetric dynamo fields
Authors: Lortz Dietrich , Meyer‐Spasche Rita , Törnig W.
Published: March 2007

The ‘anti‐dynamo’ theorems for poloidal magnetic fields with axisymmetry and plane symmetry are generalized to the case of a compressible and time‐dependent flow in a fluid with arbitrary conductivity.
On finite element methods for convection dominated phenomena
Authors: Kikuchi Fumio , Ushijima Teruo , Fujita H.
Published: March 2007

The aim of this work is to give theoretical justification of several types of finite element approximations to the initial‐boundary value problems of first order linear hyperbolic equations. Our approximate scheme is obtained by the piecewise linear continuous finite element method for space variable, x, and the Euler type step by step integration method for time variable, t. An artificial viscosity technique, up‐stream type methods are considered within the frame work of L2‐theory. The convergence and the error estimate of the approximate solutions to the true one are discussed.
Boundary integral equations for the Helmholtz equation: The third boundary value problem
Authors: Angell T. S. , Kleinman R. E. , Hsiao G. C.
Published: March 2007

In this paper we study the application of boundary integral equation methods for the solution of the third, or Robin, boundary value problem for the exterior Helmholtz equation. In contrast to earlier work, the boundary value problem is interpreted here in a weak sense which allows data to be specified in L∞ (∂D), ∂D being the boundary of the exterior domain which we assume to be Lyapunov of index 1. For this exterior boundary value problem, we employ Green's theorem to derive a pair of boundary integral equations which have a unique simultaneous solution. We then show that this solution yields a solution of the original exterior boundary value problem.
Nontrivial periodic solutions of a nonlinear beam equation
Authors: Chang K. C. , Sanchez Luis , Rabinowitz P.
Published: March 2007

We consider the existence of a nontrivial solution of the following equation:wheregis a nondecreasing function defined on R1, satisfiesg(O) = O, and some other additional conditions.

Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]‐[8]:.
A generalized Lane‐Emden‐Fowler equation
Authors: Van Broek W. J. Den , Verhulst F. , Eckhaus W.
Published: March 2007

The nonlinear potential problem Δ ϕ = –r2m 0, n = m is studied with r ⩾ 0, n ε (½, ∞), m ε (−1, ∞) and n m > 0.

With various additional conditions we have regular and singular solutions which can be studied explicitly by homology transformation. It is proved that if m − n + 1 = 0 the solution with ϕ(0) = 1, ≠ (0) = 0 is radiusstable. Numerical analysis of a number of cases with m − n + 1 = 0 yields the same conclusion.
Monotone schemes for semilinear elliptic systems related to ecology
Authors: Leung Anthony , Rabinowitz P. H.
Published: March 2007

Semilinear elliptic systems of partial differential equations related to ecology are studied, with Dirichlet boundary conditions. Monotone sequences of functions which satisfy scalar equations are constructed so that they will converge to upper and lower bounds for the solutions of the systems. In case a related system has a unique positive solution, then these sequences will converge to the solution of the original system. Applications of the monotone sequences to uniqueness and stability are also given.
Galerkin approximations for the equation Lu + Nu = f
Authors: Göthel R. , Jones D. S.
Published: March 2007

Introducing the concept of a supercontinuous operator, we obtain a general convergence theorem for Galerkin approximations. Under the stronger assumption that N is a monotone operator with N(0) = 0, we show norm convergence of the unique Galerkin approximations to the unique solution.
Existence and uniqueness for an equation of mixed type in a rectangle
Authors: Aziz A. K. , Bell J. B. , Schneider M. , Gilbert R. P.
Published: March 2007

A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure.
Biorthogonal sequences of solutions of the generalized feller equation
Authors: Lehnigk Siegfried H. , Roach G. F.
Published: March 2007

The generalized Feller equation is a linear, autonomous, parabolic equation of a positive space variable and a time variable. Its coefficients are power functions of the space variable, and they depend on four parameters. In general, the equation is singular at the origin and at infinity. It contains as special cases the special Feller equation, the Kepinski equation, and the standard heat equation. The main objective of the present paper is to establish series expansions of solutions of the generalized Feller equation in terms of the elements of two sequences of particular solutions. The elements of one of these sequences are particular initial condition solutions. The two sequences are biorthogonal. The main result is that a solution does have the desired expansion property if and only if it has the Huygens property in some neighborhood of the origin of the time variable.
Eigenvalue bounds for elliptic operators
Authors: Lortz Dietrich , Mayer‐Spasche Rita , Törnig W.
Published: March 2007

Lower bounds for the real parts of the points in the spectrum of elliptic equations

are derived. These bounds, depending only on the diameter L of the domain G and on the maximum norm M of the coefficients a, b, are optimal. They are always positive and thus the spectrum is bounded away from the imaginary axis. This result is then used to prove an “anti‐dynamo theorem” for magnetic fields with plane symmetry in the case of a compressible steady flow surrounded by a perfect conductor.
Zur theorie rotierender und schwingender schaufelkränze in einer unterschallstromung durch einen ringkanal
Authors: Buggle G. , Meister E.
Published: March 2007

In this paper the three‐dimensional perturbation flow induced by a rotating and oscillating blade row which operates in a subsonic flow in axial direction of an annular channel is studied. The velocity potential is reduced to the infinite Hilbert space vector of Fourier coefficients of an eigen‐function expansion with respect to vanishing normal derivatives on both cylinder walls. These coefficients satisfy an infinite set of ordinary differential equations of second order after an application of a one‐dimensional Fourier transform in axial direction.

Several canonical two‐part mixed boundary value problems are then investigated by reduction to “infinite two‐by‐two‐Wiener‐Hopf functional systems”. In case of strong factorizability of certain matrix‐operator‐valued functions on the line these systems may be solved explicitely. Criteria for the factorization are not given here.
Rounding errors in numerical solutions of two linear equations in two unknowns
Authors: Stummel F. , Wendland W.
Published: March 2007

New condition numbers and stability constants for the numerical behaviour of Cramer's rule and Gaussian elimination for solving two linear equations in two unknowns under data perturbations and rounding errors of floating‐point arithmetic are established. By these means fundamental error estimates and stability theorems are proved. The error estimates are illustrated by a series of numerical examples.
Asymptotic behavior of a nonhomogeneous predator‐prey system with one diffusing and one sedentary species
Authors: Rothe F. , Hadeler K.P.
Published: March 2007

In general the predator‐prey system studied will have many equilibrium states with different “patches”, i.e. regions where the sedentary species vanishes. If one equilibrium is given, a Ljapunov functional can be constructed for a set of initial data with patches satisfying a certain compatibility condition. By the methods of Alikakos [1] and Rothe [28] this implies uniform bounds for the diffusing species in a Hölder space and the sedentary species in a Lp‐space. Considering pieces of the trajectory for time in some bounded interval and using the weak*‐topology for the sedentary species, one defines an ω‐limit set which is compact and nonvoid. Using the Ljapunov functional an asymptotic version of the differential equations is derived. It turns out that they admit only constant solutions except for a very special case. Thus convergence to the equilibrium follows.
A critical case for the solvability of stefan‐like problems
Authors: Fasano A. , Primicerio M. , Hadeler K.P.
Published: March 2007

We consider a one‐phase one‐dimensional Stefan problem with general data with the aim to investigate some open questions on existence of classical solutions. We show how existence and nonexistence are discriminated by the behavior of the initial datum in the neighborhood of the starting point of the free boundary.
Optimal control problems in diffusion processes with a nonsmooth nonlinear boundary condition
Authors: Sachs E. , Meister E.
Published: March 2007

We investigate a one‐dimensional diffusion process controlled by a nonsmooth nonlinear boundary condition. Existence and estimates of positive solutions of the differential equation are derived. We prove necessary conditions for optimal controls and apply them to two examples.
A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources
Authors: Symes W. W. , Payne L.
Published: March 2007

The determination of sources of acoustic wave motion in several dimensions from remote measurements is of considerable interest in many applications, and the underlying mathematical problem is quite ill‐posed. We separate the source determination problem into a control problem for the wave equation and an inverse mixed initial‐boundary value problem, and concentrate on the latter, in which the initial data for a solution of the wave equation are to be determined from its trace on a time‐like hyperplane. Though the geometry of this problem is simple, it exhibits some of the central analytic difficulties of more complex problems. We prove a uniqueness theorem, give examples of instability, establish regularity properties of the trace, and locate noncompact classes of stable functionals. The existence of these noncompact classes shows that the problem is “partially well‐posed”, i.e. that smoothing in all directions is not required to regularize the problem, and distinguishes it from most other ill‐posed problems, such as backwards diffusion and analytic continuation.
Periodic solutions of u'(t) = −f(u(t − 1)): Multiplicity results and small period solutions
Authors: Angelstorf N. , Kirchgassner K.
Published: March 2007

In this paper we are concerned with the differential delay equation

magnified image

For odd and continuous nonlinearities f: R → R. We want to prove existence and multiplicity criteria for so called “slowly oscillating” periodic solutions of (A).

The oddness condition is of course a rather restrictive one, but due to results of Nussbaum [9], [10] and Peters [13],[14] and numerical studies of Jürgens, Peitgen and Saupe [7] and Hadeler [6] we know that even for odd nonlinearities f (A) may display a complicated dynamical behaviour. On the other hand the oddness condition allows a classification of symmetry properties of periodic solutions of (A).
Asymptotic equipartition of energy for equations of elasticity
Authors: Sandefur J. T. , Payne L.
Published: March 2007

In this paper we give a review of the equipartition of energy results of Goldstein and Sandefur [3], [4], [5] as well as proving a new result in the case of a particular fourth order equation. These results are then applied to the equations of elasticity to give a weak asymptotic orthogonality for the shear and pressure waves. In the case of boundary value problems in the interior of a bounded domain we get weak asymptotic orthogonality in the average.
Error analysis of a numerical scheme for 3D Maxwell–Landau–Lifshitz system
Authors: Cimrák Ivan
Published: March 2007

We suggest a linear numerical scheme solving strongly non‐linear coupled Maxwell–Landau–Lifshitz (Maxwell–LL) system describing ferromagnetic phenomena. Using recent results on the regularity of the solutions to the Maxwell–LL system we are able to prove convergence and to derive the error estimates for this numerical scheme. We provide numerical examples which confirm the theoretical results. Copyright © 2007 John Wiley & Sons, Ltd.
Microwave dielectric properties of NiFe2O4 nanoparticles ferrites
Authors: Rubinger C. P. L. , Gouveia D. X. , Nunes J. F. , Salgueiro C. C. M. , Paiva J. A. C. , Graça M. P. F. , André P. , Costa L. C.
Published: March 2007

Nickel ferrite (NiFe2O4) was synthesized by the micelles mixing method, using lyophilized coconut oil. The method leads to the formation of ferrite nanoparticles. Nickel ferrite was prepared in coconut oil suspension and annealed during 4 h, at 400, 600, 800, 1000, and 1200°C. The X‐ray diffraction (XRD) was applied to investigate the nanoparticle size dependence on the annealing temperature. Complex permittivity measurements were carried out in cavity resonators at 5.0 and 9.0 GHz, using the small perturbation theory. The main result is that the real part of the permittivity decreases with increasing annealing temperatures (3.6–2.4), while the imaginary part of the permittivity varies only for the lowest annealing temperatures, remaining low for the other samples (about 10−3). The X‐ray diffractograms indicates that the nanoparticle size increase with annealing temperature, allowed the correlation between the nanoparticle size and the observed microwave dielectric response. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1341–1343, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22402
Efficient analysis of resonator by the unconditionally stable three‐dimensional iterative ADI‐FDTD method
Authors: Ye Z. B. , Du L. , Rui P. L.
Published: March 2007

In this article, the iterative alternating‐direction‐implicit finite‐difference time‐domain (ADI‐FDTD) method is used to simulate the resonator in electromagnetic field. This method is exactly the same as the original Crank–Nicolson (CN) method, while recognizing the ADI‐FDTD method as a special case of a more generalized iterative approach to solve the CN‐FDTD method, which can reduce the splitting error of the ADI‐FDTD method. Numerical results demonstrate that this 3D iterative ADI‐FDTD method can improve the accuracy of the ADI‐FDTD method by using the time step size greatly exceeding the Courant–Friedrich–Levy (CFL) limit within several iterations. As a result, much time is saved compared with CN‐FDTD method. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1473–1477, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22403
Maximizing net light pressure on a chiral sculptured thin film by selection of the vapor incidence angle
Authors: Ross Benjamin M. , Lakhtakia Akhlesh
Published: March 2007

The net light pressure on a chiral sculptured thin film, for normal incidence, can be maximized by appropriately choosing the vapor incidence angle during the fabrication of the film by physical vapor deposition. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1407–1409, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22407
Permittivity characterization from open‐end microstrip line measurements
Authors: Hinojosa J.
Published: March 2007

A broad‐band method for measuring the complex permittivity of isotropic film‐shaped materials at low microwave frequencies is presented. The characterized material is the substrate of an open‐end microstrip line used as sample‐cell. Complex permittivity is computed from S11 reflection parameter measurement of open‐end microstrip cell using analytical relationships, which decrease the computation time. Vector network analyzer and high‐quality on‐microstrip test fixture are used for the measurement bench. Measurements over 0.01 GHz–3 GHz frequency range with several nonmagnetic materials show good agreements between measured and predicted results. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1371–1374, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22410
An improved discrete complex image method for Green′s functions in multilayered media
Authors: Zhuang Lei , Zhu Guoqiang , Zhang Yunhua , Xiao Boxun
Published: March 2007

The numerical implementation of traditional discrete complex image method (DCIM) approach for spatial‐domain Green's functions (GFs) is limited to low values of ρ (ρ is the distance between the source and the field points of the GFs). Although recently a direct DCIM was introduced to obtain both near‐ and far‐field region accurately, the direct DCIM was limited to choose the paths of kz plane in free‐space layer. In this paper, an improved DCIM is introduced without any quasistatic and surface‐wave extraction. We choose a novel path of kz plane. The improved DCIM works in both the near‐ and far‐field region for multilayered media as direct DCIM does. And the method is applicable to choose the paths of kz plane in the layer where the source and field points are. The improvement makes it feasible to accelerate the calculation of spatial‐domain GFs of electrically large buried objects in multilayered media. In this paper, the method developed for the computation of GFs is used for planar structures containing both lossless and lossy media. The CPU time used to perform the improved DCIM is less than 1 s for computing the fields, with a horizontal source‐field separation from 1.6 × 103λ0 to 16λ0 (λ0 is the free‐space wavelength). © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1337–1340, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22412
An efficient metamaterial‐inspired electrically‐small antenna
Authors: Erentok Aycan , Ziolkowski Richard W.
Published: March 2007

This article presents an inexpensive, efficient, and electrically‐small antenna design that is based on a metamaterial‐inspired structure driven by an electrically‐small semi‐circular loop antenna, which is coaxially‐fed through a finite ground plane. The proposed antenna system is linearly scalable over a wide frequency spectrum. The design details and radiation characteristics of the antenna system at 300, 1580, and 6000 MHz are reported. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1287–1290, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22415
Design of a 5‐bit time delay module with left‐handed and right‐handed transmission line
Authors: Chen Lijun , Zhu Qi , Han Lu , Xu Shanjia
Published: March 2007

A 5‐bit time delay module with left‐handed and right‐handed transmission line is designed and fabricated, which can realize a minimum time delay of 100 ps and a maximum time delay of 3100 ps in 9–10 GHz frequency range. Compared with traditional transmission line time delay module, the present 5‐bit left‐handed transmission line time delay module has shown its compactness and low losses. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1256–1259, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22416
New band‐pass filter design with tapped‐line using J/K‐inverter
Authors: Yun Tae‐Soon , Hong Tae‐Ui , Lee Byungje , Choi Jin‐Joo , Kim Jin‐Young , Kim Ki‐Byoung , Lee Jong‐Chul
Published: March 2007

In this letter, a novel design method of tapped‐line gap‐coupled half‐wavelength band‐pass filter (BPF) using J‐ or K‐inverter is proposed. A model of tapped‐line is composed of shunt stub and the additional transmission line that has the electrical length of the negative value. The electrical lengths of the stub and line are functions of the line's impedance and the inverter that has a variable of filter's bandwidth. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1253–1256, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22417
Input impedance‐tuning slots of PIFA antennas
Authors: Wang Hanyang
Published: March 2007

Input impedance‐tuning methods are proposed for antenna designs of mobile communications devices. The proposed method can be applied to input impedance‐tuning of single‐band, dual‐band, and multiband planar inverted‐F antenna. The prominent feature of this impedance‐tuning method is to use an inductive‐tuning slot or a capacitive‐tuning slot, rather than the width of the grounding and feeding strips and the gap between the grounding and feeding strips, to get desirable impedance matching and bandwidth. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1464–1467, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22419
Small broadband disk‐loaded monopole antenna with a vertical ground plane
Authors: Kim Myungbum , Khang Nguyen , Woo Insang , Choo Hosung , Park Ikmo
Published: March 2007

A small broadband monopole antenna with a vertical ground plane and an electromagnetically coupled feed is presented in this paper. The antenna was formed by positioning a probe with a folded stripline under a shorted square disk. A resonance of the shorted square disk was coupled to a resonance of the probe with a folded stripline, so that the antenna had a wide bandwidth of about 37% at the center frequency of 2.313 GHz based on a VSWR ≤ 2. The antenna had dimensions of 11 mm × 11 mm × 11 mm and rectangular slits were inserted into the vertical ground plane to improve distortion of the radiation pattern. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1401–1405, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI.10.1002/mop.22422
A 1‐V, 6‐mA, 3–6 GHz broadband 0.18‐μm CMOS low‐noise amplifier for UWB receiver
Authors: Chang C.‐P. , Yen C.‐C. , Chuang H.‐R.
Published: March 2007

A 3–6 GHz broadband CMOS single‐ended LNA fabricated with the 0.18 μm 1P6M process for UWB and WLAN receiver is presented. Due to its noncascode circuit architecture, the proposed LNA can operate under 1V supply voltage and 6mA current consumption. In the UWB low band (3.1–5.15 GHz), the broadband LNA exhibit a gain of 11.7–13.7dB, noise figure less than 4.9 dB and input return loss better than 13.2 dB, respectively. From 5–6 GHz range (covering Hiperlan, 802.11a, and MBOA group B), the LNA exhibit a gain of 12.4–12.7 dB, noise figure less than 5.5 dB and input return loss better than 15.7 dB, respectively. The input P1dB and IIP3 are −20 dBm and −10.9 dBm, respectively. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1358–1360, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22428
Design of a compact dual‐band bandpass filter using trisection stepped impedance resonators
Authors: Chang Sheng‐Hsiung , Weng Min‐Hang , Kuan Hon
Published: March 2007

We propose a compact dual band bandpass filter (BPF) using trisection stepped impedance resonators (SIRs). By appropriately selecting the impedance ratio (K) and length ratio (α) of the SIR, the harmonic frequencies can be tuned for generating the dual‐passband response. The BPF has good dual‐passband performances at 2.4/5.2 GHz and has a very smaller area in comparison of previous works. Good agreement is also shown between full‐wave electromagnetic (EM) simulation and measurement. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1274–1277, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22432
2 × 2 Array with UC‐EBG ground for low RCS and high gain
Authors: He Wei , Jin Ronghong , Geng Junping , Yang Guoming
Published: March 2007

In this paper, by exploiting surrounding fractal UC‐EBG ground plane, a 2 × 2 microstrip array capable of X‐band operation is studied. Result of comparison shows that this microstrip array proposed has much lower RCS than that of 2 × 2 array with the standard ground at frequencies outside operating band within 2–18 GHz while its gain is improved in the operating band. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1418–1422, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22440