ALBERT

Notizen: In this paper we provide a theory of the asymptotic expansion for an abstract kinetic equation. We show that the modified Chapman-Enskog procedure, introduced in [19], gives the error of order of ε2, uniformly in time, on the second level of approximation and in particular that the zeroth moment of the solution (the spatial density of particles) can be approximated by the solution of the diffusion-type equation with the same accuracy. The theory is applied to several types of kinetic equations with the Fokker-Planck collision operator.

Notizen: A mathematical approach to the concept of shape of a submanifold M of a Euclidean space had previously been given by means of ‘measuring functions’ (e.g. diameter or volume) and of the derived ‘size functions’. This paper relates the study and the computation of any such size function to the structure of critical points of the associated measuring function.

Notizen: We present a Riesz-like hyperholomorphic functional calculus for a set of non-commuting operators based on Clifford analysis. Applications to the quantum field theory are described.

Notizen: We consider the system of elastic waves in three dimensions under the presence of an impurity of the medium which we represent by a real-valued function q(x) (or q(x,t)). The medium is assumed to be isotropic and occupies the whole space Ω = ∝3. We study the location of the scattering frequencies associated with such phenomenon. We conclude that there is a large region on the complex plane which is free of scattering frequencies. In the remaining region they are discrete provided that q satisfies suitable assumptions concerning its behaviour at infinity.

Notizen: We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginzburg-Landau equation can be derived. Due to the presence of continuous spectrum, classical bifurcation theory is not available to describe bifurcating solutions. Thus, we consider a modified system with artificial spectral gap, which possesses an infinite-dimensional centre manifold. The amplitude equation on this manifold is called a generalized Ginzburg-Landau equation. From previous work [18] it is known that the Fourier modes are exponentially concentrated at integer multiples of the critical wave number. Hence, the error made by this modification is exponentially small in powers of the bifurcation parameter. The approximations obtained via the generalized Ginzburg-Landau equation are valid on a much longer time scale than those obtained by using the classical Ginzburg-Landau equation as an amplitude equation.

Notizen: A review of exact solutions of discrete velocity models is given. Different methods of constructing the solutions are discussed. New methods are proposed for the stationary Broadwell model, and new class of solutions is obtained. Two-dimensional flows in channel are studied on the basis of exact solutions and analogy with the Carleman model. Explicit example of non-unique solution to a boundary value problem is given. Exact hydrodynamic equations are derived for the stationary Broadwell model. A role of the Navier-Stokes approximation is discussed in detail by comparison with these exact equations.

Notizen: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.

Notizen: The problem of determining bilinear combinations of holomorphic and antiholomorphic generalized hypergeometric type integrals left invariant under the action of the monodromy groups of the integrals is studied. In the special cases of simple Pochhammer type integrals and of twofold hypergeometric type integrals the existence and uniqueness of the bilinear invariants are proved, and the bilinear invariants are explicitly computed. Preparing the tools it is shown how to linearize and iterate representations of the braid group Bn as automorphism groups of certain free subgroups of the braid group Bn+1, and how the resulting iterated linear representations of the braid group in a natural way provide an algorithm to compute the monodromy group of generalized hypergeometric type integrals. Explicit formulae for different types of integration contours are given in the case of simple and twofold integrals.

Notizen: Periodic solutions of arbitrary period to semilinear partial differential equations of Zabusky or Boussinesq type are obtained. More generally, for a linear differential operator A(y,∂), the equation A(y,∂)u = (-1)∣γ∣∂γf(y,∂γu), y = (t,x)∊∝k×G is studied, where homogeneous boundary conditions on ∂G and periodicity conditions on t are imposed. The solutions are obtained by variational methods in anisotropic Sobolev spaces.

Notizen: The quasi-hydrodynamic carrier transport equations for semiconductors extended to Fermi-Dirac statistics are considered. It is shown that in the high injection case, these equations reduce to a drift-diffusion model with non-linear diffusion terms. The limiting procedure is proved rigorously and error estimates are shown. We compute numerically static voltage-current characteristics of a forward biased pn-junction diode and compare the curves with the corresponding characteristics obtained from the standard drift-diffusion model based on Boltzmann statistics. It turns out that there exists a so-called threshold voltage at which the behaviour of the characteristic changes. Under high injection conditions, the dependence of the current on the bias appears to be approximately polynomial. The characteristics are studied analytically for a unipolar device.

Notizen: We use Hodge-Helmholtz decompositions of weighted Sobolev spaces to solve time-harmonic exterior-boundary value problems for perturbations of the (aδd+bdδ)-system (δ: the co-differential, a, b〉0). We prove, that a Fredholm alternative holds true, the eigensolutions decay polynomially at infinity, and that the positive eigenvalues do not accumulate. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: The Neumann problem for the Laplace equation in an exterior connected plane region bounded by closed and open curves is studied. The existence of classical solution is proved by potential theory. The problem is reduced to the Fredholm equation of the second kind, which is uniquely solvable. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: A new numerical method is derived for the calculation of high-frequency asymptotic expansions of the scalar wave scattered by curved periodic structures. Optimal error estimates for this method are established. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We give a complete classification for breakdown in finite time or global existence of continuously differentiable solutions to hyperbolic systems of two first-order partial differential equations posed on a real bounded interval, with boundary damping and initial data of small magnitude. Structural bounds for the derivatives of the initial data which govern the behavior of the solution are brought to light. We isolate two classes of boundary damping: the strong damping forbids the solution to blow up after a time that we exhibit while the weak damping permits a late breakdown. The results are applied to nonlinear elasticity. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We study the large time asymptotics of solutions u(x, t) of the wave equation with time-harmonic force density f(x)e-iωt, ω≥0, in the semi-strip Ω= (0, ∞)×(0, 1) for a given f∊C∞0(Ω). We assume that u satisfies the initial condition u=(∂/∂t)u=0 for t=0 and the boundary conditions u=0 for x2=0 and x2=1, and (∂/∂x1)u=αu for x1=0, with given α, -π≤α〈∞. Let Dα be the self-adjoint realization of -Δ in Ω with this boundary condition. For -π≤α〈0, Dα has eigenvalues λj=π2j2-α2, j=1, 2, … For j≥2 these eigenvalues are embedded in the continuous spectrum of Dα, σc(Dα)=[π2, ∞]. For α≥0, Dα has no eigenvalues. We consider the asymptotic behaviour of u(x, t), t→∞, as a function of α. In the case α=0 resonances of order √t at ω=πj, j=1, 2, …, were found in References 5 and 10. We prove that for α=-π there is a resonance of order t2 for ω=0 and resonances of order t for every ω〉0 (note that 0 is an eigenvalue of D-π). Moreover, for -π〈α〈0 there are resonances of order t at ω=√λj. The resonance frequencies are continuous functions of α for -π〈α〈0 and tend to πj, j=1, 2, … as α goes to zero.On the contrary in the case α〉0 there are no real resonances in the sense that the solution remains bounded in time as t→∞. Actually in this case, the limit amplitude principle is valid for all frequencies ω≥0. This rather striking behaviour of the resonances is explained in terms of the extension of the resolvent R(κ)=(Dα-κ2)-1 as a meromorphic function of κ into an appropriate Riemann surface. We find that as α crosses zero the real poles of R(κ) associated with the eigenvalues remain real, but go into a second sheet of the Riemann surface. This behaviour under perturbation is rather different from the case of complex resonances which has been extensively studied in the theory of many-body Schrödinger operators where the (real) eigenvalues embedded in the continuous spectrum turn under a small perturbation into complex poles of the meromorphic extension of the resolvent, as a function of the spectral parameter κ2. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: No Abstract

Notizen: The global existence and uniqueness of classical solution of steady motions of a third-grade fluid provided assumptions on positivness of μ (coefficient of viscosity) and α1, γ (material coefficients) is proved. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: Integral equations associated with the basic boundary value problems for the Laplace and Stokes equations are considered. The integral operators for these integral equations are interpreted as the pseudodifferential operators, and their principal symbols are calculated. The symbols are obtained in terms of the principal curvatures and the coefficients of the first quadratic form of the boundary. As a consequence, the initial approximation is suggested for the iterative methods solving the integral equations. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: The boundary integral equation method is used to prove the convergence of the Drude-Born-Fedorov equations with variable coefficients, possibly non-smooth, to Maxwell's equations as chirality admittance tends to zero. © 1998 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: New explicit stability conditions are derived for a linear integro-differential equation with periodic operator coefficients. The equation under consideration describes oscillations of thin-walled viscoelastic structural members driven by periodic loads. To develop stability conditions two approaches are combined. The first is based on the direct Lyapunov method of constructing stability functionals. It allows stability conditions to be derived for unbounded operator coefficients, but fails to correctly predict the critical loads for high-frequency excitations. The other approach is based on transforming the equation under consideration in such a way that an appropriate ‘differential’ part of the new equation would possess some reserve of stability. Stability conditions for the transformed equation are obtained by using a technique of integral estimates. This method provides acceptable estimates of the critical forces for periodic loads, but can be applied to equations with bounded coefficients only. Combining these two approaches, we derive explicit stability conditions which are close to the Floquet criterion when the integral term vanishes. These conditions are applied to the stability problem for a viscoelastic bar compressed by periodic forces. The effect of material and structural parameters on the critical load is studied numerically. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: In order to maintain spectrally accurate solutions, the grids on which a non-linear physical problem is to be solved must also be obtained by spectrally accurate techniques. The purpose of this paper is to describe a pseudospectral computational method of solving integro-differential systems with quadratic performance index. The proposed method is based on the idea of relating grid points to the structure of orthogonal interpolating polynomials. The optimal control and the trajectory are approximated by the m th degree interpolating polynomial. This interpolating polynomial is spectrally constructed using Legendre-Gauss-Lobatto grid points as the collocation points, and Lagrange polynomials as trial functions. The integrals involved in the formulation of the problem are calculated by Gauss-Lobatto integration rule, thereby reducing the problem to a mathematical programming one to which existing well-developed algorithms may be applied. The method is easy to implement and yields very accurate results. An illustrative example is included to confirm the convergence of the pseudospectral Legendre method, and a comparison is made with an existing result in the literature. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: This article establishes the existence of a trapped-mode solution to a linearized water-wave problem. The fluid occupies a symmetric horizontal channel that is uniform everywhere apart from a confined region which either contains a thin vertical plate spanning the depth of the channel or has indentations in the channel walls; the forces of gravity and surface tension are operative. A trapped mode corresponds to an eigenvalue of the composition of an inverse differential operator and a Neumann-Dirichlet operator for an elliptic boundary-value problem in the fluid domain. The existence of such an eigenvalue is established by extending previous results dealing with the case when surface tension is absent. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notizen: In this paper an initial-boundary-value problem in one-space dimension is studied for the Broadwell model extended to a gas mixture undergoing bimolecular reactions. Techniques of semigroup of bounded positive operators in a suitable Banach space are used to prove existence and uniqueness of the solution on bounded time intervals whose length depends on the initial data. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework.Fundamental solutions G are considered that are defined only on the complement of a compact set. It turns out, however, and we present examples for this, that the more interesting results only hold if G is defined on all of ∝n or if it is a Green function for an exterior boundary value problem. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notizen: In the present paper, we deal with the long time behaviour of solutions for the generalized Benjamin-Bona-Mahony equation. By a priori estimates methods, we show this equation possesses a global attractor in Hk for every integer k≥2, which has finite Hausdorff and fractal dimensions. We also construct approximate inertial manifolds such that every solution enters their thin neighbourhood in a finite time. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.

Notizen: In the present work, the problem of electromagnetic wave propagation in three-dimensional stratified media is studied. The method of decoupling the electric and magnetic fields is implemented, and the spectral approach is adopted, componentwise, to the vector equation involving the electric field. Operational calculus of self-adjoint, positive operators in suitable Hilbert spaces is used to solve the corresponding initial value problems. The spectral families of these operators for the cases of the whole space and of a finite layer are constructed. A discussion on the applicability of the obtained results to physical problems is also included. © 1998 B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: In this paper we prove under the assumption of small initial data the global existence of a classical solution to the equations in viscoelasticity, associated with a free damping boundary condition. We also show that if we choose the initial data large enough, blow up will occur in finite time. © 1998 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We consider the thermoelastic plate system,utt-γΔutt+Δ2u+αΔθ=0,θt-κΔθ-αΔut=0 and we make a comparison between the models in which γ=0 and γ〉0. We conclude that in the first case the plate system is of a parabolic type, while when γ〉0 the corresponding system has a hyperbolic behaviour. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: This paper concerns the orbital stability for solitary waves of the Long Wave-Short Wave resonance equations. Since the abstract results of Grillakis et al. [7, 8] cannot be applied directly, we can extend the abstract stability theory and use the detailed spectral analysis to obtain the stability of the solitary waves. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: We consider particle transport in a three-dimensional convex region V, bounded by the regular surface ∂V. We assume that particles are specularly reflected by ∂V and that a source q is assigned on ∂V; more general non-homogeneous boundary conditions are also discussed. The problem is non-linear because the boundary condition is not homogeneous. We prove existence of a unique strict solution and by using the theory of semigroups we derive the explicit expression of such a solution in terms of the boundary source q. In the appendix, we indicate how some properties of affine operators can be used to derive the solution. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: A phase-field model based on the Coleman-Gurtin heat flux law is considered. The resulting system of non-linear parabolic equations, associated with a set of initial and Neumann boundary conditions, is studied. Existence, uniqueness, and regularity results are proved. An asymptotic analysis is also carried out, in the case where the coefficient of the interfacial energy term tends to 0. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: We apply the Child-Langmuir asymptotics of the Vlasov-Poisson system to the case of a bipolar diode, i.e. a vacuum diode where two species of particles of opposite electric charge are flowing. This leads to a simplified model which, if at least one of the two injected currents is not too large, has a unique solution. Moreover, in that case, the currents flowing inside the diode are limited by the so-called bipolar Child-Langmuir currents. In the case of large currents, other solutions may appear, and the formation of virtual electrodes may occur inside the diode. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: In this paper we consider the Cauchy problem for the equation∂u/∂t + u ∂u/∂x + u/x = 0 for x 〉 0, t ≥ 0, with u(x, 0) = u0-(x) for x 〈 x0, u(x, 0) = u0+(x) for x 〉 x0, u0-(x0) 〉 u0+(x0). Following the ideas of Majda, 1984 and Lax, 1973, we construct, for smooth u0- and u0+, a global shock front weak solution u(x, t) = u-(x, t) for x 〈 φ(t), u(x, t) = u+(x, t) for x 〉 φ(t), where u- and u+ are the strong solutions corresponding (respectively) to u0- and u0+ and the curve t → φ(t) is defined by dφ/dt (t) = 1/2[u-(φ(t), t) + u+(φ(t), t)], t ≥ 0 and φ(0) = x0.© 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: A variational approach to a non-linear non-local identification problem related to the non-linear transport equation is studied. Introducing a similarity transformation, the problem is formulated as an identification problem for a non-linear differential equation of second order with an additional non-local condition. For the solution of the forward problem stability in H1-norm with respect to the identification parameter is obtained. Using this result the existence of a solution to the identification problem is proved. Some results of computational experiments are given. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: We consider the plate equation in a polygonal domain with free edges. Its resolution by boundary integral equations is considered with double layer potentials whose variational formulation was given in Reference 25. We approximate its solution (u, (∂u/∂n)) by the Galerkin method with approximated spaces made of piecewise polynomials of order 2 and 1 for, respectively, u and (∂u/∂n). A prewavelet basis of these subspaces is built and equivalences between some Sobolev norms and discrete ones are established in the spirit of References 14, 16, 30 and 31. Further, a compression procedure is presented which reduces the number of nonzero entries of the stiffness matrix from O(N2) to O(N log N), where N is the size of this matrix. We finally show that the compressed stiffness matrices have a condition number uniformly bounded with respect to N and that the compressed Galerkin scheme converges with the same rate than the Galerkin one. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: The relativistic Vlasov-Maxwell-Fokker-Planck system is used in modelling distribution of charged particles in plasma. It consists of a transport equation coupled with the Maxwell system. The diffusion term in the equation models the collisions among particles, whereas the viscosity term signifies the dynamical frictional forces between the particles and the background reservoir. In the case of one space variable and two momentum variables, we prove the existence of a classical solution when the initial density decays fast enough with respect to the momentum variables. The solution which shares this same decay condition along with its first derivatives in the momentum variables is unique. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: We consider reactive mixtures of dilute polyatomic gases in full vibrational non-equilibrium. The governing equations are derived from the kinetic theory and possesses an entropy. We recast this system of conservation laws into a symmetric conservative form by using entropic variables. Following a formalism developed by the authors in a previous paper, the system is then rewritten into a normal form, that is, in the form of a quasilinear symmetric hyperbolic-parabolic system. Using a result of Vol'pert and Hudjaev, we prove local existence and uniqueness of a bounded smooth solution to the Cauchy problem. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: Approximate solutions of the non-linear Boltzmann equation, which have the structure of the linear combination of three global Maxwellians with arbitrary hydrodynamical parameters, are considered. Some sufficient conditions which allow the error between the left- and the right-hand sides of the equation tend to zero, and which are calculated either in the mixed metric or in the pure integral metric, are obtained. The class of the distributions, which minimized this error for the arbitrary Knudsen number, is found. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: The paper considers a system of partial differential equations of convection dispersion type, modelling a stratified two-phase fluid flow. Local existence in time is proved for a sufficiently smooth initial data, given in the set of physically admissible states. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: In this paper we study the motion of an elastic conducting wire in a magnetic field. The motion of the conductor induces a current in the wire (Faraday's law) which, in turn produces a force on the wire. We consider the linear equation obtained by linearizing the resulting equations of motion about an equilibrium solution. This is a hyperbolic partial differential equation with a non-local term. We prove existence and uniqueness of a weak solution of an initial-boundary value problem for this equation. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: In this paper we are concerned with a weighted least-squares finite element method for approximating the solution of boundary value problems for 2-D viscous incompressible flows. We consider the generalized Stokes equations with velocity boundary conditions. Introducing the auxiliary variables (stresses) of the velocity gradients and combining the divergence free condition with some compatibility conditions, we can recast the original second-order problem as a Petrovski-type first-order elliptic system (called velocity-stress-pressure formulation) in six equations and six unknowns together with Riemann-Hilbert-type boundary conditions. A weighted least-squares finite element method is proposed for solving this extended first-order problem. The finite element approximations are defined to be the minimizers of a weighted least-squares functional over the finite element subspaces of the H1 product space. With many advantageous features, the analysis also shows that, under suitable assumptions, the method achieves optimal order of convergence both in the L2-norm and in the H1-norm. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: We consider the two-parameter non-linear Sturm-Liouville problems. By using the variational method on general level sets, the variational eigenvalues are obtained. The purpose of this paper is to study the properties of these variational eigenvalues with respect to the parameter of general level sets. © 1998 B. G. Teubner Stuttgart - John Wiley & Sons, Ltd.

Notizen: An explicit factorization of the Fourier symbol matrix functions generated by Sommerfeld diffraction problems with oblique derivatives is obtained. For this purpose a new prefactorization procedure is developed which makes use of factorization through weighted L2 spaces. These results yield a representation of a generalized inverse of the corresponding matrix Wiener-Hopf operator and the asymptotic behaviour of the solution at the edge of the screen. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We study a high-field version of the periodic Schrödinger-Poisson system, for which the Poisson equation includes nonlinear terms corresponding to a field-dependent dielectric constant. Using a Galerkin scheme, we prove global existence and uniqueness, and present the matrix equations for the numerical evaluation of the potential. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: A generalized Hele-Shaw flow is derived and analysed in injection and compression moulding which contains non-isothermal and non-Newtonian rheological behaviour of the molten polymers as well as non-symmetric effects. The corresponding fixed domain formulations for the flow are investigated from a mathematical point of view. Different approaches for the determination of the temperature and some viscosity models are discussed. Together with an outline of the proposed solution algorithm special finite element techniques are described for the numerical treatment of this complex non-linear moving boundary problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: The Ginzburg-Landau equation which describes nonlinear modulation of the amplitude of the basic pattern does not give a good approximation when the Landau constant (which describes the influence of the nonlinearity) is small. In this paper a derivation of the so-called degenerate (or generalized) Ginzburg-Landau (dGL)-equation is given. It turns out that one can understand the dGL-equation as an example of a normal form of a co-dimension two bifurcation for parabolic PDEs. The main body of the paper is devoted to the proof of the validity of the dGL as an equation whose solution approximate the solution of the original problem. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: The paper deals with the Dirichlet problem for the Stokes linear equation in a domain exterior to an open surface. With the help of the theory of boundary integral (pseudo-differential) equations uniqueness and existence theorems are proved in the Bessel-potential and Besov spaces and Cα-smoothness (with α〈1/2) of solution is established in the neighbourhood of the boundary of the open surface. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: In this paper the authors consider the initial boundary value problem of the ferromagnetic spin chain equation and prove the existence of the global attractor and finiteness of the Hausdorff and the fractal dimensions of the attractor. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We regard the Schrödinger-Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrödinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. As a tool we develop a Riesz-Dunford functional calculus for semibounded self-adjoint operators using paths of integration which enclose a real half-axis. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We investigate an initial-value problem modelling fragmentation processes where particles split into two or more pieces at a rate, γ, that not only depends on the sizes of the particles involved but also on time. The existence of non-negative, mass-conserving solutions is established by considering a truncated version of an associated non-autonomous abstract Cauchy problem. The latter has solutions of the form u(t)=Un(t,t0)f, t≥t0, where f is the known data at some fixed time t0≥0 and {Un(t,s)}t0≤s≤t≤T is a uniformly continuous evolution system. A limit evolution system {U(t,s)}t0≤s≤t≤T is shown to exist. Depending on the form of the known data f at time t0, the scalar-valued function u, obtained from the limit evolution system via u(x, t)=[U(t, t0)f](x) for a.e. x〉0, t≥t0, is a solution of either the original initial-value problem or an integral version of this problem. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: We study the boundedness and a priori bounds of global solutions of the problem Δu=0 in Ω×(0, T), (∂u/∂t) + (∂u/∂ν) = h(u) on ∂Ω×(0, T), where Ω is a bounded domain in ∝N, ν is the outer normal on ∂Ω and h is a superlinear function. As an application of our results we show the existence of sign-changing stationary solutions. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: In this note we investigate spatial bounds for the heat conduction equation with three relaxation times. We use energy methods similar to those considered in the study of the backward parabolic heat equation. Finally, we show that for any positive choice of the coefficients we may take initial data for which the solution is unstable when we suppose that the body is bounded. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The process is vital in a waste water treatment plant, where the particles consist of several biological components. The concentrations of these are modelled by a one-dimensional system of conservation laws with source term. It is shown how a unique solution can be obtained, and how analytical solutions are used to form a conservative numerical algorithm. © 1997 B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: This paper is concerned with the existence and uniqueness of the steady-state solution of hydrodynamic model for semiconductor devices. Boundary conditions are prescribed by vorticity on inflow boundary as well as by electron density, temperature, and normal component of electron velocity on whole boundary. If the ambient temperature is large, and if both vorticity on inflow boundary and the variation of density on boundary are small, a unique subsonic solution exists. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: The theory of high-frequency waves has been used to calculate first and second-order asymptotic solutions for the propagation of non-linear waves in a cylindrical symmetric flow of an electron plasma. The behaviour of acceleration waves and weak shock waves has been analysed through these solutions and Whitham's rule for a weak shock wave on any wavelet has been confirmed through the first-order solution. The appearance of a weak shock wave on any wavelet has been determined and its strength, the location, and the speed of propagation have been found from the asymptotic solution presented in this paper. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.

Notizen: During postnatal development of the pigeon, a large portion of the skeleton becomes pneumatized, displacing the hemopoietic bone marrow. The consequences of pneumatization on distribution and quantity of bone marrow as well as the availability of other sites for hemopoiesis have been investigated. Hemopoietic marrow of differently aged pigeons divided into five groups from 1 week posthatching (p.h.) up to 6 months p.h. was labeled with Fe-59 and examined by serial whole-body sections. Autoradiography and morphometry as well as scintillation counts of single bones and organs were also carried out. No sign of a reactivation of embryonic sites of erythropoiesis was found. Bone marrow weight and its proportion of whole-body weight increased during the first 4 weeks p.h. from 0.54% to 2.44% and decreased in the following months to about 1.0%. The developing bone marrow showed a progressive distribution during the first months of life, eventually being distributed proportionally over the entire skeleton, except for the skull. At the age of 6 months p.h. bone marrow had been displaced, its volume decreasing in correlation to increasing pneumaticity and conversion to fatty marrow. This generates the characteristic pattern of bone marrow distribution in adult pigeons, which shows hemopoietic bone marrow in ulna, radius, femur, tibiotarsus, scapula, furcula, and the caudal vertebrae.

Notizen: Artificially incubated fertile eggs from wild alligators have a significantly better hatch rate than those of captive, pen-reared alligators, possibly due to differences in the morphology of the eggshells. We compared the morphology of eggshells of wild alligators to those of captive alligators living in semi-natural environmental pens. Lengths and widths of eggs were measured and volume was determined, assuming an ellipsoid shape. Eggs were also evaluated for the quality of the eggshell (the presence or absence of rough deposits). Pieces of shell were cut from unincubated eggs and from eggs incubated for 55 days (just before hatching) and examined by scanning electron microscopy. Open pores on the outer surface of the shells were counted and thickness of the pieces was measured from micrographs. Results indicated that the number of pores on eggshells was lowest in eggs of captive alligators with early embryonic death. The number of pores was intermediate in eggs with early embryonic death from wild alligators, and the number of pores was highest in eggs with full-term embryos from wild or captive alligators. It is suggested that decreased porosity of eggshells may be associated with early embryonic death, is more prevalent in captive animals, and may, therefore, be related to poor hatch rate among penreared alligators.

Notizen: Adult hornets (Vespa orientalis; Hymenoptera, Vespinae) build the brood combs out of organic or mineral matter. The cement that serves to glue the building material together is secreted in their saliva, the latter hardening within seconds to form fibers or plates. This saliva-derived spittle overlies and unites the building particles laminally and vertically. The hornet larvae spin a cocoon within the brood cells, which is largely fastened to and supported by the cell walls and is composed of a network of silk fibers and interlinking flat surfaces. On the outside of the cocoon fibers are spherical button-like structures that are very rich in phosphorus. The chemical composition of the adult salivary cement and the larval cocoon fibers is similar: both contain the elements P, Mg, S, Cl, K, and Ca. The possible biological significance of these findings is discussed.Among social insects belonging to the Hymenoptera, there are three main groups that build a multitude of cells, namely, the paper wasps (Polistinae), the other social wasps or hornets (Vespinae), and the social bees (Apinae). The constructed cells serve mainly for rearing the brood, but in many instances (particularly among various Apinae) they also serve for storing honey and pollen. For building material, Apinae rely primarily on beeswax (a product secreted by the bee itself to which various amounts of plant resins are added). On the other hand, wasps (Polistinae and Vespinae) build mainly from matter collected in the nearby environment, be it organic matter such as tree bark, mineral matter, or a combination of the two.Much information has accumulated on comb and cell building among these insect groups (e.g., Wheeler, '23; Van der Vecht, '57, '65; Lindauer, '61; Michener, '61; Kemper and Döhring, '67; Wilson, '71; Guiglia, '72; Spradbery, '73; Edwards, '80; Brian, '83; Schremmer et al., '85). Species of Polistinae and Vespinae are prevalent in forest areas in Southeast Asia and in central and South America or in the temperate regions in both the northern and southern hemispheres, and they mainly use vegetable matter to build their combs. In contrast, species prevalent in the Mediterranean region, which is dry and relatively unvegetated during the wasp and hornet active season, rely more on nearby mineral than on plant matter. Comb building in the Oriental hornet is well known (Darchen, '64; Ishay et al., '67; Schaudinischky and Ishay, '68; Ishay, '73, '75a, b, '76; Ishay and Sadeh, '75, '76; Ishay and Perna, '79; Ishay et al., '82). Recently Ganor et al. ('86) described the cell wall in the V. orientalis comb, showing it to be composed of mineral particles collected near the subterranean nest, in contrast to the comb of two European species (V. crabro and Vespula) (Paravespula) germanica, which is built primarily of organic matter. Regardless of whether the building material is mineral or organic, the hornets utilize particles of sand or other minerals or pieces of wood wrapped and melded together by saliva. However, nothing is known about the cement or mortar used to glue together these “bricks.” The present investigation was initiated to increase our knowledge of this cementing substance.Combs of V. orientalis were collected from fields in the Tel-Aviv district in 1987 during the active season, which extends over most of the summer months. Because the combs are easily damaged, care was taken to remove them intact from the natural nest. Once removed, the combs were cleared of the existing brood (eggs, larvae, or pupae) and then stored carefully in dry glass vessels until examined. For the present study, combs were collected only from nests in Khamra soil, which is common in the Tel-Aviv district and along the coastal area of Israel. To investigate the morphology of the cement material in the comb, strips of comb wall as well as segments of the pupal silk dome were removed from each comb and prepared for examination. The comb wall strips were cut to a size of 3 × 6 mm and fastened to the stub of a scanning electron microscope (SEM). The silk pieces were processed in two ways: (1)strips of 3 × 4 mm were fastened onto a stub with the convex (outer surface) facing up or (2) with the concave (interior) side upward.Silk strips were boiled for 2 hours in distilled water to remove all impurities, such as foreign matter adhering to the silk secreted by the larvae. Examination of these silk fibres was carried out in the three ways: (1)SEM micrography of the exterior (white portion) of the silk dome; (2) micrography of the interior; (3) micrography of both exterior and interior aspects after boiling for 2 hours in distilled water to remove water-suspended foreign materials that may have clung to the silk dome in the course of ordinary nest activity.The chemical composition of selected specimens was investigated by x-ray analysis. They were done on JEOL 840 Scanning Electron Microscope (SEM) equipped with Link 10,000 Energy-Dispersive System (EDS). (With the EDS System, the spectrometer separates the elements according to energy rather than wavelength). Quantitative analysis was by ZAF4 program. Five strips of comb cell wall were examined from a randomly selected comb, each comb from a different nest. Micrographs were taken of isolated silk samples from each of the examined combs.

Notizen: Dissections were performed to document buccal anatomy in three species of the pulmonate genus Helisoma Swainson, 1840. The 28 muscles which are responsible for radular feeding in these animals are organized in three concentric and integrated envelopes. The deepest of these includes muscles which manipulate the radula about the odontophoral cartilage. Elements of the middle envelope direct movements of the cartilage within the buccal cavity, and muscles of the outer envelope control movements of the buccal mass within the cephalic haemocoel. Motion analysis by videomicrography showed that muscles of the middle and outer envelopes contribute to the action of radular feeding by acting as antagonists to other muscles and to hydrostatic elements of the buccal apparatus. Observations of radular dentition showed that although each of the three species examined has a unique radula, especially with regard to the specific details of tooth shape, all resemble a radula characteristic of the Planorbidae with regard to other, more general, aspects of ribbon architecture.

Notizen: Crocodilians and birds are the extant representatives of a monophyletic taxon known as archosaurs. Their limbs are highly derived in terms of reduction in number of skeletal elements in both the carpus and the tarsus. It is necessary to have a detailed description of crocodilian limb ontogeny to address the evolutionary issue dealing with the origin and organization of the avian limb. In this paper, we present an analysis of the early development of the crocodilian limb skeleton. Contrasting with earlier observations, we redefine the number and composition of carpal, tarsal, and phalangeal elements. This ontogenetic information is then used to introduce a revision of the homologies of the skeletal elements in the crocodilian limb. Some invariances are pointed out in the developmental organization of tetrapod limbs and this evidence serves to readdress several issues concerning the evolution of the avian limb. We present further embryological data in support of the hypothesis that digits 2-3-4 are the components of the wing skeleton in birds. In general, our comparative survey indicates that the elements that appear late in ontogeny are the ones lost in phylogeny. By comparing turtle (primitive) limb development with crocodilian and bird development, we propose a hypothesis in which the derived skeletal patterns found in crocodilians and birds have originated by a heterochronic process of paedomorphosis.

Notizen: A unique pathway that utilizes endoplasmic reticulum (ER) networks is proposed for screening pigment granule formation in the retina of adult Eumesosoma roeweri. Smooth endoplasmic reticulum (SER) functions to transport pigment particles to the formative site. Each site is composed of concentric, interconnected rings of SER that are filled with dense-cored, spherical pigment particles. Formation of the screening pigment granule begins by the release of particles from the innermost rings of carrier SER. Continued release followed by fusion and condensation of the pigment particles results in the formation of a mature pigment granule.

Notizen: Light and scanning electron microscopy of vascular replicas from the facultative air-breathing fish Heteropneustes fossilis show modifications in the macrocirculation of the respiratory organs and systemic circulation, whereas, gill microcirculation is similar to that found in typical water-breathing fish. Three and sometimes four ventral aortae arise directly from the bulbus. The most ventral vessel supplies the first pair of arches. Dorsal to this another aorta supplies the second gill arches, and a third, dorsal to, and larger than the other two, supplies the third and fourth arches and the air sacs. Occasionally a small vessel that may be the remnant of a primitive aortic arch arises from the first ventral aorta and proceeds directly to the mandibular region without perfusing gill tissue. The air sac is perfused by a large-diameter extension of the afferent branchial artery of the fourth gill arch and its circulation is in parallel with the gill arches. Blood drains from the air sac into the fourth arch epibranchial artery. A number of arteries also provide direct communication between the efferent air sac artery and the dorsal aorta. All four gill arches are well developed and contain respiratory (lamellar) and nonrespiratory (interlamellar and nutrient) networks common to gills of water-breathing fish. Air sac lamellae are reduced in size. The outer 30% of the air sac lamellar sinusoids are organized into thoroughfare channels; the remaining vasculature, normally embedded in the air sac parenchyma, is discontinuous. A gill-type interlamellar vasculature is lacking in the air sac circulation. Despite the elaborate development of the ventral aortae, there is little other anatomical evidence to suggest that gill and air sac outflow are separated and that dorsal aortic oxygen tensions are maintained when the gills are in a hypoxic environment. Physiological adjustments to hypoxic water conditions probably include temporal regulation of gill and air sac perfusion to be effective, if indeed they are so.

Notizen: The antennae of adult Damalinia ovis, the sheep louse, were studied using light and scanning electron microscopy. Sensory structures are located on all three antennal segments with the predominant sensilla type being tactile. Nine different types of sensilla are described on the basis of external appearance. One of the sensilla, designated a “pit organ” because of its unusual shape, has not been described previously. A pair of these sensilla are present on each antenna, and their function is unknown. A group of 11 sensilla on the tip of each antenna contains olfactory and chemosensory pegs, and a possible thermohygroreceptor. The antennae are sexually dimorphic, the male having more tactile sensilla, two well-developed terminal hooks, and a different cuticular architecture on the posterior surface of antennal segment 1.

Notizen: The formation of the unpaired structure ventral to the basibranchial region, the so-called urohyal, differs within osteichthyans. A cartilaginous preformed, unpaired “urohyal” is present in sarcopterygians. A three-tendon ossification is present in Polypterus. An “urohyal” or urohyal is absent in both Amia and Lepisosteus. The urohyal formed as an unpaired ossification of the tendon of the sternohyoideus muscle is a feature of teleosts. A new structure, the parurohyal, arises as a double ossification of the tendon of the sternohyoideus muscle in siluroids; during ontogeny an anterodorsal crest or cup-like structure derives from the anterior basibranchial region and the tendon bone; therefore, the parurohyal is compound in origin. Judging from their formation and their distribution within osteichthyans the cartilaginous preformed “urohyal” and the teleostean urohyal are nonhomologous, whereas the urohyal and parurohyal are homologous. The urohyal is connected by ligaments with the ventral hypohyals in most teleosts, whereas it articulates with the ventral hypohyals in teleosts such as Anguilla and Chanos. The parurohyal is a synapomorphy of siluroids. The parurohyal in siluroids is articulated with both ventral and dorsal hypohyals, and with the basibranchial region in catfishes such as diplomystids and ictalurids, whereas it articulates only with the ventral hypohyals in other catfishes such as trichomycterines. The passage of the hypobranchial artery through the hypobranchial foramen of the parurohyal is a unique feature of siluroids, like the absence of the basihyal bone.An ossified dorsal hypohyal appears late in ontogeny in Amia, as do tooth plates related to the medial side of the hyoid arch and branchiostegal rays in Amia, and tooth plates on the hyoid arch and branchiostegal rays in Elops (unique features within extant teleosts). Two ossified hypohyals, a synapomorphy of teleosts, are present early in ontogeny.There is intraspecific variation in the onset of ossification of the bones of the head, but the sequence of ossification between bones in a defined structural system is conserved (e.g., branchiostegal rays ossify first, then bones of the hyoid arch).

Notizen: The vas deferens of Ambystoma macrodactylum is composed of a peritoneal epithelium, connective tissue layer with fibroblasts, circular smooth muscle, capillaries, cells containing lipid, and a luminal epithelium composed of a single layer of cuboidal cells covered by a net of interconnected ciliated squamous cells. The cuboidal cells have abundant rough endoplasmic reticulum, mitochondria, and PAS + secretory vesicles. Squamous cells of breeding males consistently have tufts of ∼100 cilia located at one end of the long axis of each cell. These cilia may help distribute secretory products. The squamous cells, absent in post-breeding males, are apparently sloughed into the lumen. Lipid vesicles are present throughout the cytoplasm of the cuboidal and squamous epithelial cells and are also in some cells of the connective tissue layer. These vesicles increase dramatically in number during the first 4 weeks after breeding and may serve as an energy pool for the next breeding season. Enzyme-histochemical tests for testosterone synthesis were negative. In addition to the accumulation of lipid and the loss of squamous cells in the vas deferens, after breeding PAS + vesicle production is terminated. These alterations appear to represent energy conservation strategies employed by the sperm-depleted vas deferens.

Notizen: The concept of parallel muscle combinations, in which spindle density is significantly higher in small muscles compared to their larger counterparts in large-small muscle combinations acting across a joint, is supported by the results of this study regardless of the joint. Analysis of the canine data as well as previously published guinea pig forelimb and human pelvic limb data revealed no significant difference in spindle density between antigravity and non-antigravity muscles. Furthermore, a gradual increase in spindle density from proximal to distal on the limb was not found, although spindle density was significantly higher in the intrinsic manus or pes muscles compared to more proximal limb muscles in all three species. The significant differences in spindle densities in parallel muscle combinations and in manus/pes versus proximal muscles are discussed relative to their possible role in the control of locomotion.

Notizen: The choanocyte chambers of eight different haplosclerid sponge species have been investigated with regard to their histological structure, their relation to the mesohyl, and their arrangement between the canal systems. Two fundamentally different organizational types occur in the investigated sponge species. In Haliclona rosea, H. oculata, H. elegans, H. simulans, H. rava, H. fistulosa, and Acervochalina limbata the choanocytes are separated from the mesohylar tissue, being more or less covered over the outer surface by pinacocytes belonging to the incurrent canal walls. In Haliclona indistincta, on the other hand, the choanocytes are, as in most other Demospongiae, in contact with the mesohyl at their outer surfaces. This indicates that the present order Haplosclerida is polyphyletic and contains sponges of a presumably poecilosclerid origin.

Notizen: The three-dimensional structures of the carotid labyrinth in five species of anurans representing four families (Rana nigromaculata, Rana catesbeiana, Bufo japonicus, Hyla arborea, and Xenopus laevis), and three species of caudates representing three families (Cynops pyrrhogaster, Hynobius nebulosus, Ambystoma mexicanum) were compared using vascular corrosion castings and scanning electron microscopy (SEM). Anuran carotid labyrinths are spherical in shape and are classified into two groups according to the origin of the external and internal carotid arteries. One group, which included Rana, Hyla, and Bufo, is characterized by the presence of a vascular ring at the proximal end and some vascular routes at the distal end of the labyrinth. The external and internal carotid arteries originate from these structures. The other group, which includes only Xenopus, is characterized by the external carotid artery opening directly from the central chamber or the common carotid artery, and by the internal carotid artery originating from within the vascular maze. The vascular maze is most complex in Xenopus, less so in Rana and Bufo, and simplest in Hyla. The carotid labyrinths in Cynops and Hynobius are oblong in shape. The fundamental organization in salamanders is similar to that in anurans. The vascular maze, however, is much simpler than in Hyla. There is no specialized swelling in Ambystoma mexicanum. The present findings suggest that most amphibian carotid labyrinths have the appropriate architecture for controlling vascular tone.

Notizen: The vomeronasal sensory epithelium of a crotaline snake, Trimeresurus flavoviridis, was shown to consist of a superficial supporting cell layer and an underlying sensory cell layer composed of columns of sensory cells. The supporting cell layer consists of both supporting cells and dendrites of the underlying sensory neurons. The apical regions of sensory cell dendrites contain numerous microtubules, many elongated mitochondria, centrioles, and electron-dense bodies. The dendrites terminate as dendritic knobs from which microvilli project into the vomeronasal lumen. Smooth vesicles are abundant in the dendritic terminals and their vicinity. Supporting cells also bear microvilli, and these cells contain large electron-opaque granules and dense vesicles near their free surfaces. Cytoplasmic extensions of the supporting cells form a meshwork which separates dendrxites from each other in the vicinity of the luminal surface. The meshwork becomes obliterated in the infranuclear region of each supporting cell. Bipolar-shaped sensory cells with lightly stained round nuclei contain the characteristic cell organelles of neurons and are thought to be sensory neurons. These cells are especially characterized by well-developed lamellae of rough endoplasmic reticulum and extensive arrays of smooth endoplasmic reticulum. The perikarya of cells located in the apical region of the cell columns tend to contain larger amounts of smooth endoplasmic reticulum and lipofuscin granules than the perikarya of cells located in lower regions. Undifferentiated cells are found in the basal region of the columns. Satellite cells form the framework of the columns and are also found among neuronal elements.

Notizen: The protandric hermaphrodite Ophryotrocha puerilis possesses one pair of eyes. They are located in the peristomium. Each light-sensitive organ consists of one sensory cell and one to two supporting cell(s) embedded in a cup-shaped reflector. The sensory-supporting cell complex is enveloped by a basal lamina. This lamina is supposed to be identical with the neural lamella. Thus the eyes proper have to be regarded as protrusions from the brain, while epidermal cells seem to differentiate to crystalline cells (reflector) and are deposited onto the sensory complex.The reflector is built up by several cup-shaped cells (juveniles, 4-5; adults, 10-12). Each of these cells comprises a multilayer of parallel-oriented, membrane-bound crystalline platelets which are thought to be guanine. The sensory cell is of the inverted rhabdomere type. Submicrovillar cisternae, typical for most polychaete eyes, are lacking. The first and always present supporting cell entirely envelops the sensory cell, thus forming the extracellular space around the rhabdomere. It does not contain any pigment granules. Often but not always a second supporting cell has been observed surrounding the sensory cell and first supporting cell. It is interpreted as a glial cell.In the sensory cell beneath the rhabdomere, pino- and phagocytosis can be observed and secondary lysosomes are found in high densities. Preliminary results seem to demonstrate that there is no distinct diurnal cycle of receptoral membrane recycling. In comparison with the ocelli of Dinophilidae, which have been interpreted as a dorvilleid-related family, morphological differences and their application to phylogenetic considerations are discussed.

Notizen: The appearance pattern of pharyngeal tooth germs was investigated in the larval Japanese dace, Tribolodon hakonensis, which has a bilaterally asymmetrical dentition. Teeth develop in a series of replacement waves beginning with the initial central tooth (Ce) and continuing with teeth of anterior (An) and posterior (Po) positions relative to the initial one. Identified by wave number (n) and tooth position (r), according to the formula n-1[r], tooth germs appeared in the order of tooth 0[Ce0], 1[Po1], 1[Anl], 2[Ce0], 2[An2], 3[Po1], 3[An1], 4[Ce0], 4[An2], 5[Po1], 5[An1], 5[An3], 6[Ce0], 6[An2] during the larval period. Dentition on the right side, however, lacks the first tooth at position An2 (tooth 2[An2]) and teeth at position An3. Tooth germs on the first, second, and third replacement waves appeared simultaneously on the arches of both sides. During following waves, tooth germs on the left side appeared later than those on the right. Delay of tooth germ appearance On the left side is interpreted as an inhibitory influence of existing tooth germs in accordance with Osborn's (Proc. R. Soc. Lond. Ser. B 179:261--289, '71) theory. The delay of tooth germ appearance on the left arch is most pronounced on the seventh replacement wave. Teeth of the right major row in adults of this species are replaced more frequently than those of the left major row, apparently in correlation with the absence of the first larval tooth at position An2 and teeth at position An3. It is hypothesized that cyprinids evolved the minor rows and specialized teeth of their adult dentition as apomorphic characteristics by the process of neoteny.

Notizen: Development of the internal structures of the caudal region (muscles, bones, cartilages, nerves, and blood vessels) of the Da/Da mutant medaka and of wild-type +/+ fish was compared. Muscles and nerves were immunochemically stained by using an antibody to troponin T and antibodies to neurofilament proteins, respectively. Bones and cartilages were stained with alizarin red and alcian blue. In stages 31-32 of the Da/Da embryo, the rudiments of epurals 1, 2, and 3 differentiated dorsally opposite the sites of the ventral rudiments of the parhypural, the lower hypural plate, and the upper hypural plate, respectively. In the +/+ embryo, the rudiments of epurals 1 and 2 differentiated in the later developmental stages (after stage 34), but the rudiment of epural 3 did not differentiate. In the Da/Da embryo, the deep dorsal flexor passed dorsalwards and ended at the rudiment of epural 2, whereas the muscle passed ventralwards and ended at the rudiment of the upper hypural plate in the +/+ embryo. In the Da/Da fry, the epichordal region of the caudal fin fold grew and the notochord extended straight into the tail without bending, while in the + /+ fry, the epichordal region did not grow and the notochord turned dorsalwards within the tail. In the Da/Da fry, extra skeletal rudiments and musculature differentiated in the epichordal region of the caudal fin, whereas these supernumerary structures did not develop in the +/+ fry. The pattern of the epichordal skeleton and musculature in the caudal region of the adult Da/Da fish was an almost mirror-image duplication of the hypochordal structures. These observations suggest that the characteristic expansion of the dorsal fin and epichordal lobe in the caudal region of the adult Da/Da fish is due to a process of ventralization, whereby the dorsal skeleton, musculature, and fin fold are stimulated to differentiate in a pattern like that which is restricted to the anal fin and hypochordal lobe of the wild type.

Notizen: Tongue musculature in 24 genera of snakes was examined histologically. In all snakes, the tongue is composed of a few main groups of muscles. The M. hyoglossus is a paired bundle in the center of the tongue. The posterior regions of the tongue possess musculature that surrounds these bundles and is responsible for protrusion. Anterior tongue regions contain hyoglossal bundles, dorsal longitudinal muscle bundles and vertical and transverse bundles, which are perpendicular to the long axis of the tongue. The interaction of the longitudinal with the vertical and horizontal muscles is responsible for bending during tongue flicking. Despite general similarities, distinct patterns of intrinsic tongue musculature characterize each infraorder of snakes. The Henophidia are primitive; the Scolecophidia and Caenophidia are each distinguished by derived characters. These derived characters support hypotheses that these latter taxa are each monophyletic. Cylindrophis (Anilioidea) is in some characters intermediate between Booidea and Colubroidea. The condition in the Booidea resembles the lizard condition; however, no synapomorphies of tongue musculature confirm a relationship with any specific lizard family. Although the pattern of colubroids appears to be the most biomechanically specialized, as yet no behavioral or performance feature has been identified to distinguish them from other snakes.

Notizen: Wall and internal organelles of the encysting salt marsh heterotrich ciliate Fabrea salina were examined by bright field and Nomarski interference contrast microscopy and by transmission and scanning electron microscopy. A mucoid sheath believed to be derived from bacteria covers the ectocyst. The possible bacterial origin of this sheath has been demonstrated experimentally by its removal and reappearence after 24 hours. Control ectocyst maintained in sterile seawater did not replace the sheath. The ectocyst has a crinkled appearance. The endocyst is composed of two layers. The inner endocyst material is continuous with that of the plug located at one end of the cyst. The two membranes are separated from one another by an interwall space filled with fibrous material. The cytoplasm, covered by an outer double membrane pellicle, contains mucocysts, pigment granules, microtubules, non-ciliated kinetosomes, Golgi complexes, ribosome-studded endoplasmic reticulum, and mitochondria. The endoplasm contains numerous autophagosomes, mitochondria, and food reserve materials. The macronucleus is centrally located in the cytoplasm of the encysting organism.

Notizen: Analysis of lateral and dorsoventral radiographic films shows that ingestion, transport, and mastication in Pedetes capensis (Rodentia) are cyclic and their movement patterns are essentially similar for the three food types offered. During the ingestion cycle, closing of the mouth is accompanied by a backward translation of the condyles, so that movement is predominantly orthal. During the opening stage, the extent of the anterior condylar translation is smaller. As a result the mandibular incisors move ventrally and posteriorly. During the ingestion cycles, food is transported to the back of the tongue, with the transverse rugae and the folds of the upper lip playing important roles.Springhares show a bilateral masticatory pattern; food is chewed on both sides simultaneously. During chewing, the condyles lie in their most forward position at maximum opening of the mouth. The mouth is closed by rotation of the lower jaw around the temporomandibular joint coupled with posterior condylar translation. At the beginning of the slow-closing stage, the upward rotation of the mandible slows and the jaw slowly shifts forward. During the grinding stage, the mandible is shifted forward with both toothrows in occlusion. During the opening stage, the jaw returns to its starting position.Comparison of kinematic and anatomical data on rodent mastication suggests that some dental characteristics form the most important factors regulating the masticatory pattern and consequently allow reasonably reliable prediction of rodent masticatory patterns.

Notizen: Avian embryos can be completely paralyzed by injection of neuromuscular-blocking agents. We used a single injection of decamethonium iodide to paralyze embryos at 7, 8, or 10 days of incubation and analyzed the growth of individual bones (clavicle, mandible, ulna, femur, tibia, humerus) and of individual muscles that act upon some of those bones (clavicular and sternal heads of m. pectoralis, and mm. biceps brachii, depressor mandibulae, pseudotemporalis, and adductor externus). Growth of the bones is not equally affected by paralysis. Only 27% of clavicular growth (by mass) but 77% of mandibular growth occurred in paralyzed embryos, whereas the four long bones exhibited 52-63% of their normal growth. Analysis of muscle weight, fiber length and physiological cross-sectional area (weight/fiber length) indicate that there was greater reduction of the muscles acting on the limbs than of those acting on the mandible, i.e., diminished growth of the skeleton is correlated with reduced muscular activity. Specific retardation of clavicular growth is due to fusion of sternal rudiments and collapse of the thorax, as well as virtual absence of the musculature that normally attaches to the clavicle. We discuss these results in the light of intrinsic and extrinsic factors governing growth of tne embryonic skeleton. Paralysis reduces skeletal growth by reducing both the movements taking place in ovo, and the loads imposed on the bones by muscle contraction, changes that represent alterations in the mechanical environment of the skeleton.

Notizen: This study using light and electron microscopy indicates that the saccus vasculosus is distinguishable in 9-mm embryos and grows continuously throughout embryonic development to the adult stage. In the saccus vasculosus, epithelial mitoses are observed in all stages studied. Phases of centriologenesis, ciliogenesis, and globule formation have been characterized in developing coronet cells. During the phase of centriologenesis, new centrioles appear in association with pre-existing centrioles and not on deuterosomes. After ciliogenesis, each cilium differentiates to a globule almost at the same time as the other cilia of the coronet cell. The inner membrane system of the globules seems to derive from the ciliary plasma membrane. This membrane system often produces membrane whorls during the development. The different phases of coronet cell development have been found in the same individual and in all the stages studied except the 9-mm embryo. Cerebrospinal fluid-contacting neurons are observed in the saccus epithelium from the 12-mm embryos on and are distinguishable from coronet cells in their early formative stages. The three cell types of the saccus vasculosus increase continuously in number during development. Nerve processes are found in the saccus vasculosus of embryos, whereas differentiated synapses appear later in the fry. The significance of continued coronet cell formation is discussed in relation to a putative coronet cell and/or a globule renewal cycle in the adult.

Notizen: Changes of architecture of adult rat gastrocnemius medialis muscle (GM) due to growth were studied in relation to length-force characteristics. Myofilament lengths were unchanged, indicating constant sarcomere length-force characteristics. Number of sarcomeres within fibers was unchanged as a consequence of growth, allowing persistence of differences between proximal and distal fibers in all age groups. Distal fiber length at muscle optimum length was shorter for the 14- than for the 10- and 16-week age groups despite a lack of difference of number of sarcomeres. This is indicative of a shift of optimum fiber length with respect to muscle length to lengths higher than optimum length. Some evidence for the occurrence of distribution of fiber optimum lengths with respect to muscle optimum length was found in other age groups as well, albeit of a smaller magnitude. Muscle and aponeurosis length increased substantially with growth. Functional effects of increased aponeurosis lengths were increased contributions to muscle length changes by the aponeurosis, allowing smaller fiber contributions in older animals. Fiber angle increased approximately 5° with growth. Despite the differences of architecture indicated above, muscle length range between optimum length and active slack length was constant. This was probably caused by widening of this length range in the youngest age group by variations of architecture within the muscle. It is concluded that adaptation of aspects of muscle architecture is an important mechanism for adult muscle growth in rat GM. Of these aspects regulation of muscle length seems a dominant factor.

Notizen: The cupula of the supraorbital neuromast in the lateral line canal of the clown knifefish contains vertical columns. In the central region of the cupula overlying the macula, these columns are densely packed, are relatively constant in size, and run from the base of the cupula to the surface of the cupula which is exposed to canal fluid. There are two types of columns, dark and light, which form elliptical compartments in planes of section that cut across the columns; the cupula therefore has the appearance of mosaic tile in such sections. The dark compartments contain tubules that extend from the base of the cupula at the junction with the macula to the top of the cupula. Each tubule is associated with the kinocilium of a single hair cell. The lateral parts of the cupula, not overlying the macula, also contain compartments, but these compartments differ in size and structure from those in the central region. In addition to the compartments, the central region of the cupula also contains spherical aggregates of droplets. These small aggregates, termed mora, are found principally in a layer within the central region of the cupula, but are also found outside this layer. Because of their light-reflecting properties, the mora can be used for noninvasive optical measurements in vivo of the motion of the cupula.

Notizen: Light and electron microscopic examination demonstrated two types of non-endocrine agranular cells, cavity boundary cells and stellate cells, in the adenohypophysis of the South American lungfish, Lepidosiren paradoxa. The cavity boundary cells line the hypophyseal cleft and diverticulum and display few microvilli, occasional cilia, prominent junctional complexes, and many cytoplasmic microfilaments. The stellate cells are scattered in the glandular parenchyma and are devoid of microvilli and cilia. When adjacent, they are connected to one another by desmosomes. Pinocytotic vesicles or caveolae are frequently seen along the plasma membrane of the agranular cells adjoining the endocrine cells or abutting on the basement membrane. Possible roles of the agranular cells, physically and metabolically supportive functions, are discussed on the basis of their ultrastractural features.

Notizen: The paired organ of Bellonci protrudes from the optic lobe of the giant Antarctic isopod, Glyptonotus antarcticus. It is linked to the cortex by a broad peduncle. No connection to the cuticle or “sensory pore organ” was found. A cluster of sensory-like cells forms two outer ciliary segments branching into numerous microvilli with microtubules. The putative sensory somata are irregular in shape and contain a very high density of glycogen granules. The two outer segments sprout from two pits of the soma in different directions, forming a right angle. Glial cells wrap around the sensory cells and also delimit lacunae into which bundles of microvilli project. These lacunae contain electron-dense granules of small size and with species-specific patterns. Lacunae and dense granules show features typical of a degeneration process in the sensory cells.This general morphology corresponds to the unilobular type of organ of Bellonci, known in other isopods; it differs from the plurilobular type with onion bodies found in other Crustacea.

Notizen: Neuromast structure in Rana cancrivora larvae was observed by scanning and transmission electron microscopy. Neuromast units, each being composed of two or three neuromasts, are arranged in several well-defined lines in the head, body, and tail regions. The structure of neuromasts in these three regions is basically identical. The neuromast is composed of sensory, sustentacular, and mantle cells. The top of each neuromast has a hillocklike appearance, and is surrounded by four to six epidermal cells with tight intercellular junctions. Long kinocilia and many stereocilia occur in the apex of the neuromasts and are surrounded by numerous microvilli. Numerous granules are present on the apical portions of the mantle and the sustentacular cells. Four or five trapeziform mantle cells are connected closely with each other to form the shell of the neuromast. Large intercellular spaces occur between the mantle cells and the cells of the inner epidermal layers, and between the cells of the inner epidermal layer. Thus, at the apical parts of the neuromast intercellular junctions are tight and the intercellular spaces are more dilated in more basal areas. Morphologically the neuromasts of R. cancrivora larvae resemble those of generalized pond anurans, based on the grouping of Lannoo (Journal of Morphology 191:115-129, 1987a), although larvae of this species inhabit brackish water.

Notizen: Orbital gland structure of the Atlantic bottlenose dolphin, Tursiops truncatus, was examined at the macroscopic, light microscopic, and electron microscopic levels. The gland completely encircles the ocular globe in a belt-like fashion near the conjunctival fornix but is considerably more developed medially. Duct openings are scattered throughout the fornix and over the surface of the palpebral conjunctiva. Microscopically, the gland has a tubuloalveolar arrangement; alveolar cells contain numerous secretory vesicles which can be interpreted as two structural types by light and electron microscopy. Histochemical staining demonstrates that both types contain glycosaminoglycans. Lipid analysis of the glandular secretion (dolphin tears) shows them to be non-oily and to contain only negligible amounts of cholesterol, triglycerides, phospholipids, and free fatty acids. The secretion is clear, slippery, and viscoelastic and well-adapted to protecting the eye and to reducing frictional forces between the eye surface and surrounding seawater.

Notizen: The muscle fibers of the feline biceps femoris have tapered ends, across which tension is transmitted to the endomysium. The angle of taper of 11 ends, measured on scanning electron micrographs, varied between 0.16° and 1.18°. The muscle fibers are highly variable in cross-sectional shape. The shape of the fibers has been quantified as the ratio (form factor [FF]) of the measured perimeter to the calculated circumference of a circle having an area equal to that contained by the fiber perimeter. The FF for 173 terminal portions of fibers varied between 1.06 and 1.85 and was found to have a highly significant negative correlation with sarcomere length. The slope of the regression line suggests that the fibers maintain both volume and surface area as they change length. These studies suggest that isovolumic muscle fibers maintain a constant surface area by changing shape as they change length.

Notizen: Salt glands of the domestic duck Anas platyrhynchos differ from those of the herring gull Larus argentatus and other birds. In ducks, each salt gland consists of distinct medial and lateral segments. Centrally located drainage ducts that extend along the entire length of these medial and lateral segments collect hypertonic fluid secreted by an array of lobules. Each lobule is formed by a single mass of branched tubules in which the direction of capillary blood flow is opposite to that of the secreted fluid. This fluid drains from the medial segment through an external duct that opens into the nasal cavity at the base of the vestibular fold. A duct from the lateral segment loops and opens onto the surface of the nasal septum. The structure and function of the secretory cells is reviewed briefly within the context of our study of the configuration of duck nasal salt glands.

Notizen: A contrast radiographic study of pelvic fin drainage in rays reveals considerable differences in patterns of drainage among the species studied. The “typical” shark pattern of drainage, to the lateral abdominal vein, is also found in rays with shark-like morphology. However, variation in the connections of pelvic fin veins to muscular and cutaneous vessels of the pectoral fin occurs in the more “derived” batoid groups, with marked differences between rays of similar external morphology and mode of locomotion. There is a positive association between the pattern of fin drainage and the number of radial cartilages in the posterior (metapterygial) lobe of the pectoral fin. Variation in shark pelvic fin drainage may also be related to differences in pectoral fin morphology.

Notizen: Dissections of Sudan black B stained specimens reveal that, of a complex of medial, intermediate, and lateral muscles of skates, presumed homologous to the cucullaris of sharks, only the lateral muscle is innervated by a branch or branches of the vagus and is inserted, in part, to the fused pharyngobranchials of the caudal visceral arches. The medial and intermediate muscles are supplied by separate branches of rostral spinal nerves and do not attach to the branchial skeleton. The lateral muscle therefore is the most likely homologue of the cucullaris (trapezius) of sharks and perhaps other fishes and tetrapods. The medial and intermediate muscles appear to be part of the axial musculature.

Notizen: An immunocytological study of four different parts of the gut of Helix aspersa clearly demonstrates the presence of many cells and fibers immunoreactive toward antibodies directed to vertebrate (α, β-endorphin, α, β-MSH, ACTH 1-24 and ACTH 17-39, met-enkephalin, somatostatin, insulin, glucagon, P.P., serotonin) or invertebrate (FMRF-amide) peptides.These results are evidence of the presence of different substances related to known peptides or amines in the epithelial and connective tissue cells and nerve fibers of the snail gut. Immunocytochemistry may help to elucidate the morpho-functional characteristics of the enteroendocrine cells of H. aspersa.

Notizen: A histochemical investigation of kidney and lower intestine of the European starling (Sturnus vulgaris) shows no carbonic anhydrase activity in proximal convoluted tubules, although activity is seen in similarly prepared sections of rat proximal tubules. Early distal tubule cells in the starling are stained throughout the cytoplasm and at the apical and highly infolded basolateral membranes. Late distal tubules lose apical activity and have reduced basolateral infolding, resulting in less intense staining. Darkly stained intercalated cells appear in the connecting tubules and cortical collecting ducts. Both of these segments also show intense basolateral staining. Medullary cones of the starling are highly organized, with central zones containing unstained thin descending limbs of loops of Henle, surrounded by both medullary collecting ducts with only scattered cells staining for enzyme, and by thick ascending limb segments. The latter contain many uniformly stained cells intermingled with occasional unstained cells. Scattered cells of the starling colonic villi demonstrate intense apical brush border membrane staining as well as cytoplasmic staining. Cells lining the cloaca stain less intensely. A biochemical assay for carbonic anhydrase was used to quantify enzyme activity in these tissues. Starling kidney contained 1.96 ± 0.33 (mean ± SEM) enzyme units/mg protein, less than half the activity seen in rat kidney. Stripped colonic epithelium contained 0.66 ± 0.15 enzyme units/mg protein. These quantitative results correlate well with the interpretations derived from the histochemical observations. The lack of proximal tubule carbonic anhydrase activity suggests that the avian kidney relies more on distal nephron segments to achieve net acidification of the urine.

Notizen: The orientation of the fibers in the dermis of the tiger salamander, Ambystoma tigrinum, undergoes a dramatic repatterning at metamorphosis. The pre-metamorphic, larval dermis is a tight layer composed of crossed fibers that wind helically around the trunk. This condition is retained by neotenic adults which do not undergo metamorphosis. In contrast, the metamorphosed adult dermis consists of a superficial, loose network of fibers invested with large multicellular glands - -the stratum spongiosum - and a deeper tight layer of fibers - the stratum densum. However, unlike the crossed fibers of the pre-metamorphic dermis, there is no preferred orientation to the fibers in either layer of the post-metamorphic dermis.In order to evaluate whether these two distinctly different fiber patterns are constructed from biochemically similar fibers, the collagen types present in the pre- and post-metamorphic dermis were determined using SDS-polyacrylamide gel electrophoresis. Type I collagen is the predominant collagen of the dermis and the same major collagen types are present for all individuals, whether preor post-metamorphic. Thus, the major types of collagen that compose the dermal fibers do not change during metamorphic repatterning of the dermis.