In part I of this work we defined a Titchmarsh-Weyl-coefficient M(X) for singular I( hermitian systems of arbitrary deficiency index. This construction proceeded by the method of von Nmmann for selfadjoint extensions of symmetric operators. In this part we show how a Titchmarsh-Wuyl coefficient f i ( X ) defined by a limit of Titchmarsh-Weyl coefficiente on compact intervals is Iuliited to our M(X). Examplea are given in the intermediate deficiency index case which show that IWI. all limits of Titchmarsh -Weyl coefficients on compact intervals give rise to a singular selfadjoint Iiwblern. I . IntroductionIn [7] the Titchmarsh -Weyl coefficient was defined for separated selfadjoint boundnry conditons for a singular Shermitian system. This was accomplished by a con-~t.ruction using the von Neumann theory of selfadjoint extensions of symmetric opernl.ors. For the details concerning the assumptions and the notations we refer to [7], wj)ecially to Theorem 4.7.The traditional method of defining the Titchmarsh -Weyl coefficient is to define it for a regular problem on a compact subinterval [a,c] of [a,b) and then investigate the Jliriit for c -t b. In the minimal deficiency index case, that means 76 = 0 (for the tldinition of q, see (3.1) in [7]) the method is quite satisfactory, since the limit for v --+ b is unique and independent of the boundary condition imposed on the regular lriidpoint c. This method can also be made satisfactory for the maximal deficiency Itidex case, that is n = m. For details we refer to [4, 51 as well as to [2].

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MACI in the PF joint with concurrent correction of PF maltracking if required leads to similar clinical and radiological outcomes compared with MACI on the femoral condyles.

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Demyelinating disorders, characterized by a chronic or episodic destruction of the myelin sheath, are a leading cause of neurological disability in young adults in western countries. Studying the complex mechanisms involved in axon myelination, demyelination and remyelination requires an experimental model preserving the neuronal networks and neuro-glial interactions. Organotypic cerebellar slice cultures appear to be the best alternative to in vivo experiments and the most commonly used model for investigating etiology or novel therapeutic strategies in multiple sclerosis. Areas covered: This review gives an overview of slice culture techniques and focuses on the use of organotypic cerebellar slice cultures on semi-permeable membranes for studying many aspects of axon myelination and cerebellar functions. Expert opinion: Cerebellar slice cultures are probably the easiest way to faithfully reproduce all stages of axon myelination/demyelination/remyelination in a three-dimensional neuronal network. However, in the cerebellum, neurological disability in multiple sclerosis also results from channelopathies which induce changes in Purkinje cell excitability. Cerebellar cultures offer easy access to electrophysiological approaches which are largely untapped and we believe that these cultures might be of great interest when studying changes in neuronal excitability, axonal conduction or synaptic properties that likely occur during multiple sclerosis.

We consider the differential equation (*I -u"+ x ( x ) u = p 2 f p ( x ) u on a finite interval I, where I contains m turning points, that is here, zeros of 9. Using asymptotic estimates proved by R. E. LANGER for solutions of (*) for intervals containing only one turning point we derive asymptotic estimates (for p -+ co) for a special fundamental system of solutions of (*) in I. The results obtained are fundamental for the investigation of eigenvalue problems defined by (*) and suitable boundary conditions.

IV (Case series).

Recently my attention was directed to the tubercle-like growths on roots of Cycas revoluta. A cursory examination showed that they were infested by a nostoc. In my search for the literature on the subject I found few and incomplete references.Between I 870 and I 873 Reinke discovered parasitic Nostocaceae in species of Gunnera and Cycas. Janczewski discovered parasitic algae in mosses, Cohn in Lemna, Kny in Florideae and Strasburger in Azolla.Reinke is to my knowledge the only person calling attention to an Anabaena found parasitic in a specialized parenchyma layer of Cycas roots. His incomplete though exact description has induced me to study the subject more closely.Cycas root tubercles, which are simply short somewhat enlarged dichotomously branched rootlets, are quite common on most of our cultivated cycads. They occur on young as well as on old plants. The youngest plants at my disposal were about two years old. Only a few tubercles were present. A large, well nourished plant about twenty-four years old had many tubercles.They were most numerous near the surface of the soil; a few were wholly above and some were found a foot or more below the surface. Usually they are formed from the ends of rootlets, sometimes from the side of root branches, especially the single unbranched tubercles. In position they show evidence of negative geotropism. This is very marked in tubercles near the surface of the soil. Branching is always dichotomous (see plate III, fig. 3). Branches are short and somewhat spindle-shaped, the ends being bluntly rounded. Why they should branch dichotomously is interesting.It is probably a form of atavism showing the relation of cycas to the vascular cryptogams.Likewise the occasional dichotomous branching of leguminous tubercles may indicate a descent from cryptogams. 1 As to color one may readily distinguish 'It may be mentioned here that the relative positions of the phloem and xylem in the vascular system of leguminous tubercles corresponds to that in Cycas.