Über analytisch abhängige holomorphe und meromobphe Abbildungen

We discuss the conceptions of analytic dependence, strict analytic dependence, spaces of level sets and complex bases of holomorphic mappings and their relationship. For instance, a theorem of the following type is proved: Let X be a normal complex space, let be holomorphic mappings, which are analytically related (i.e. depends analytically on and depends analytically on). Let be maximal (i.e. majorizes every holomorphic map which is strictly analytically dependent on) and let be strongly maximal (i.e. majorizes every holomorphic map which depends analytically on). Then Z^* is a proper modification of, if is proper or nowhere degenerated.     

Chaotic behavior in deformable models: the double-well doubly periodic oscillators

The motion of a particle in a one-dimensional perturbed double-well doubly periodic potential is investigated analytically and numerically. A simple physical model for calculating analytically the Melnikov function is proposed. The onset of chaos is studied through an analysis of the phase space, a construction of the bifurcation diagram and a computation of the Lyapunov exponent. The parameter regions of chaotic behavior predicted by the theoretical analysis agree very well with numerical simulations.     

Analytically invariant spectral resolvents of closed operators

The concept of analytically invariant subspace, in the framework of spectral resolvents, is extended to unbounded closed operators. One obtains necessary and sufficient conditions for a spectral resolvent to be analytically invariant. An application, concerning a strong type of spectral decomposition for closed operators with the spectra on the real line, concludes this study.     

A scheme for stable numerical differentiation

A method for stable numerical differentiation of noisy data is proposed. The method requires solving a Volterra integral equation of the second kind. This equation is solved analytically. In the examples considered its solution is computed analytically. Some numerical results of its application are presented. These examples show that the proposed method for stable numerical differentiation is numerically more efficient than some other methods, in particular, than variational regularization.     

Formal and analytic linearizability of families of conformal map germs (ℂ, 0) → (ℂ, 0)

We consider a nondegenerate one-parameter family of germs of conformal maps of (?, 0) into (?, 0). We prove that such a family is analytically linearizable whenever it is formally linearizable. In this case, the linearizing coordinate change analytically depends on the parameter.     

Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer

The spectral radius ρ of the matrix integral operator defining the covariance matrix of a standard vector Monte Carlo estimate in the polarized radiative transfer problem is examined. The theory of positive operators is used to analytically calculate ρ = ρ₀ for transfer through an infinite homogeneous medium. For a bounded medium, it is shown that ρ is approximately equal to ρ₀ times the spectral radius of the operator corresponding to radiative transfer without polarization. This is shown numerically by estimating the iterations of the corresponding resolvent and approximately analytically by using a perturbation of a special functional.     

Adaptive synchronization of fractional Lorenz systems using a reduced number of control signals and parameters

This paper analyzes the synchronization of two fractional Lorenz systems in two cases: the first one considering fractional Lorenz systems with unknown parameters, and the second one considering known upper bounds on some of the fractional Lorenz systems parameters. The proposed control strategies use a reduced number of control signals and control parameters, employing mild assumptions. The stability of the synchronization errors is analytically demonstrated in all cases, and the convergence to zero of the synchronization errors is analytically proved in the case when the upper bounds on some system parameters are assumed to be known. Simulation studies are presented, which allows verifying the effectiveness of the proposed control strategies.     

Curvilinear airfoil optimization of extremal drag force in hydro-aerodynamics

Direct and inverse boundary value problems are solved and the solution of an optimization problem is obtained analytically in the case of some nonlinear integral functionals. The plane potential flow of an inviscid fluid is considered in the absence of mass forces (Hyp). The flow – unlimited jet – encounters a symmetrical curvilinear obstacle (the Helmholtz scheme). For inverse problems there are derived singular integral equations and the movement is obtained in the auxiliary canonical half plane. Next, an optimization problem is solved analytically. The design of the optimal airfoil is performed. The drag coefficient and other geometrical parameters are computed in the case of a given distribution of the velocity on the profile. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chaos in a three-species food chain model with a Beddington–DeAngelis functional response

This paper investigates a three-species food chain model with a Beddington–DeAngelis functional response, both analytically and through numerical simulations. First the equilibrium states of the system are identified and their stability analyzed analytically. The results of simulations demonstrate chaotic long-term behavior over a broad range of parameters. The existence of a strange attractor and computation of the largest Lyapunov exponent also demonstrate the presence of chaotic dynamics in the model.     

An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq fluid, which is heated and salted from below in the presence of Soret coefficient is studied analytically using both linear and nonlinear stability analyses. The normal mode technique is used in the linear stability analysis while a weak nonlinear analysis based on a minimal representation of double Fourier series method is used in the nonlinear analysis. The generalized Darcy model including the time derivative term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameters, solute Rayleigh number, Soret parameter and Lewis number on the stationary, oscillatory, finite amplitude convection and heat and mass transfer are shown graphically.     

Sur les notions de quasi-homogénéité de feuilletages holomorphes endimension deux

In this note, we recall the different notions of quasi-homogeneity for singular germs of holomorphic foliations in the plane presented in [6]. The classical notion of quasi-homogenity allude to those functions which belong to its own jacobian ideal. Given a foliation in the plane, asking that the equation of the separatrix set is a classical quasi-homogeneous function we obtain a natural generalization in the context of foliations. On the other hand, topological quasi-homogeneity is characterized by the fact that every topologically trivial deformation whose sepatrix family is analytically trivial is an analytically trivial deformation. We give an explicit example of a topological quasi-homogeneous foliation which is not quasi-homogeneous in the sense given above.

     

On certain alternating boundary-layer solutions to singularly perturbed parabolic equations

The solution to a special singularly perturbed parabolic problem with a right-hand independent of the spatial variable is studied numerically and analytically.     

An analytic invariant of ordinary curve singularities

It is well known that analytically equivalent ordinary plane curve singularities have projectively equivalent tangent cones. In this note we introduce an analytic invariant in order to show two non analytically equivalent ordinary 5-fold points with projectively equivalent (or equal) tangent cones.

     

The distributional dimension of fractals

In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.     

Zur Fortsetzungsaufgabe des Prandtlschen Stempelproblems und einiger damit verwandter Fälle

Summary The semi-graphical complete solutions proposed byBishop for the Prandtl indentation problem and forV-notched bars in two-dimensional plastic flow are treated analytically. Applying directly the integration method of Riemann for second boundary value problems of hyperbolic differential equations to the slip-line fields in the rigid regions some exact results are derived and discussed; eventually the collapse load corresponding to both cases is analytically confirmed.     

Rimming flow of a power-law fluid: Qualitative analysis of the mathematical model and analytical solutions

Rimming flow of a non-Newtonian fluid on the inner surface of a horizontal rotating cylinder is investigated. Simple lubrication theory is applied since the Reynolds number is small and liquid film is thin. For the steady-state flow of a power-law fluid the mathematical model reduces to a simple algebraic equation regarding the thickness of the liquid film. The qualitative analysis of this equation is carried out and the existence of two possible solutions is rigorously proved. Based on this qualitative analysis, different regimes of the rimming flow are defined and analyzed analytically. For the particular case, when the flow index in a power-law constitutive equation is equal to 1/2, the problem reduces to the fourth order algebraic equation which is solved analytically by Ferrari method.     

Light tail asymptotics in multidimensional reflecting processes for queueing networks

We are concerned with the stationary distributions of reflecting processes on multidimensional nonnegative orthants and other related processes, provided they exist. Such stationary distributions arise in performance evaluation for various queueing systems and their networks. However, it is very hard to obtain them analytically, so our interest is directed to analytically tractable characteristics. For this, we consider tail asymptotics of the stationary distributions.     

Geometric exponents and Kleinian groups

Suppose is the limit set of an analytically finite Kleinian group and that is an enumeration of the components of . Then This had been conjectured by Maskit. We also define a number of different geometric critical exponents associated to a compact set in the plane which generalize the index of Besicovitch and Taylor on the line. Although these exponents may differ for general sets, we show that they are all equal when is the limit set of a non-elementary, analytically finite Kleinian group and they agree with the classical Poincaré exponent. Oblatum 30-X-1995 & 11-III-1996     

两自由度非对称三次系统非线性模态的奇异性质

利用非线性模态子空间的不变性和摄动技术,研究两自由度非对称三次系统在奇异条件下系统的性质.重点考虑子系统之间线性耦合退化时的奇异性质.对于非共振情形,所得到的解析结果表明,系统出现单模态运动以及振动局部化现象,这种现象的强弱不但与非线性耦合刚度有关,而且与非对称参数有关.并解析地得到了参数的门槛值;对于1:1共振情形,模态随非线性耦合刚度和非对称参数的变化会出现分岔,得到了参数分岔集以及模态的分岔曲线.