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1. The blue-green alga Anacystis nidulans was cultured under steady state conditions at 25 and 39 degrees C. and under several different light intensities to give five different types of cells. 2. Cells were submitted to pigment analysis based upon acetone extracts and aqueous extracts obtained by sonic disintegration. The different cell types show a… (More)

- Wolfgang Arendt, Werner Kratz, Alan McIntosh, Dieter Beschorner

In the first part inequalities for solutions of Riccati matrix difference equations are obtained which correspond to the linear Hamiltonian difference system ⌬ X s A X q B U , ⌬U s C X y A T U , k k k q 1 k k k k kq1 k k where A , B , C , X , U are n = n-matrices with symmetric B and C. If the k k k k k k k matrices X are invertible, then the matrices Q s U… (More)

We consider symplectic difference systems involving a spectral parameter together with general separated boundary conditions. We establish the so-called oscillation theorem which relates the number of finite eigenvalues less than or equal to a given number to the number of focal points of a certain conjoined basis of the symplectic system. Then we prove… (More)

In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the… (More)

In this paper we prove the differentiability properties of solutions of nonlinear dynamic equations on time scales with respect to parameters. This complements the previous work of the first and third authors regarding the existence and continuity of solutions with respect to parameters. In addition, we treat separately time scale dynamic equations which… (More)

- Jack Myers, W. A. Kratz
- The Journal of General Physiology
- 1955

Anac.ystis n~ulans is a small blue-green alga which has many of the attributes desired in an experimental organism for photosynthetic studies. Reliable culture media and characteristics of its growth, photosynthesis, and respiration have been described (Kratz and Myers, 1955a, b). In exploratory studies it was noted that both the shape of the light… (More)

In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same… (More)

- Werner Kratz, Markus Tentler, Werne Kratz
- 2007

In this article we treat the algebraic eigenvalue problem for real, symmetric, and banded matrices of size N × N , say. For symmetric, tridi-agonal matrices, there is a well-known two-term recursion to evaluate the characteristic polynomials of its principal submatrices. This recursion is of complexity O(N) and it requires additions and multiplications… (More)