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  • 1
    Digitale Medien
    Digitale Medien
    On the existence of positive solutions for semilinear elliptic equations with Neumann boundary conditions (1995)
    Springer
    Probability theory and related fields 101 (1995), S. 251-276 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 35J65 ; 60J65 ; 53C21
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in unbounded Lipschitz domainsD ⊂ ℝ d (d≥3), having compact boundary, with nonlinear Neumann boundary conditions on the boundary ofD. For this we use an implicit probabilistic representation, Schauder's fixed point theorem, and a recently proved Sobolev inequality forW 1,2(D). Special cases include equations arising from the study of pattern formation in various models in mathematical biology and from problems in geometry concerning the conformal deformation of metrics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01375828
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  • 2
    Digitale Medien
    Digitale Medien
    Cytochrome P-450 suggestions as to the structure and mechanism of action (1970)
    Springer
    Naturwissenschaften 57 (1970), S. 69-72 
    Details
    ISSN: 1432-1904
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Chemie und Pharmazie , Allgemeine Naturwissenschaft
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00590682
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  • 3
    Digitale Medien
    Digitale Medien
    The natural selection of the chemical elements (1997)
    Springer
    Cellular and molecular life sciences 53 (1997), S. 816-829 
    Details
    ISSN: 1420-9071
    Schlagwort(e): Key words. Elements; environment; evolution; natural selection; prokaryotes; eukaryotes; multicellular organisms.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Medizin
    Notizen: Abstract. Evolution is treated here in a novel way. DNA or any other code is considered to be conservative and therefore, once life began, it would prevent change. Change was imposed upon the DNA code as a stress resulting in vulnerability to 'advantageous' DNA damage and mutation. In this respect it is the stress, the changing environment, that opened up a possibility of evolution once an early life form had optimised itself in primitive circumstances. Here I examine the initial slow-coming-to-terms with the environment of primitive life, and then its evolution as the environment forced the DNA into novel development by introducing chemical elements in new forms. The situation today is no different. Environmental change is hostile to present day life and will lead to further evolution.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s000180050102
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  • 4
    Digitale Medien
    Digitale Medien
    A physico-chemical approach to morphogenesis: the roles of inorganic ions and crystals (1988)
    Springer
    Cellular and molecular life sciences 44 (1988), S. 638-650 
    Details
    ISSN: 1420-9071
    Schlagwort(e): Morphogenesis and inorganic crystals ; crystal morphology ; amorphous solids ; membrane enzymes ; tubulins ; filamentous structures ; equilibrium growth ; crystals ; acantharia ; radiolaria ; desmids ; loxodes
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Medizin
    Notizen: Summary We consider morphogenesis with special references to the development of mineral frameworks, organic filamentous structures and the location of enzymes, including ion-pumps, in membranes. Starting from a description of the morphology of inorganic crystals we analyse so-called equilibrium growth, i.e. growth at constant shape, both outside and inside biological systems. It is shown that an initial small spherical cell in which linear, ordered, inorganic or organic features are built will become distorted. The distortion is due to stresses which affect membrane curvature and consequently rearrange enzymes in membranes. The cell system can rapidly attain a steady-state of development, (‘equilibrium’) growth, of fixed morphology. After a considerable growth period the cell may cease to grow or the steady state may be broken and a transition can then occur to a quite new morphology. Examples are taken mostly from unicellular organisms but the ideas apply to multi-cellular systems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01941024
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  • 5
    Digitale Medien
    Digitale Medien
    Protein dynamics studied by NMR (1993)
    Springer
    European biophysics journal 21 (1993), S. 393-401 
    Details
    ISSN: 1432-1017
    Schlagwort(e): NMR ; β-sheets ; α-helices ; dynamics ; protein-actions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Physik
    Notizen: Abstract The results of NMR studies using several nuclei indicate that proteins have considerable internal mobility. The most obvious is the mobility of side-chains. This mobility is general on the exterior surfaces but extends internally in a differential way. The functional value of surface mobility concerns both on and off rates of ligand binding (e.g. metal ions and parts of substrates) and protein/protein interactions. The mobility, which indicates that recognition is more in the hand-in-glove class than in the lock-in-key class, makes for a modified view of the specificity of protein interactions. Thus, fast on/off systems cannot be as selective as slower systems. Segmental mobility of proteins is considered in the context of protein secondary structure. The least mobile segments are the β-sheet and the tight β-turn. Mobility is always possible for, but not within, rod-like helices and in loose turns. Many examples are given and the importance of mobility in molecular machines is described. Finally, examples are given of virtually random-coil proteins, segments, and linker regions between domains and the functional value of such extremely dynamic regions of proteins is discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00185866
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  • 6
    Digitale Medien
    Digitale Medien
    Reflected Brownian motion with skew symmetric data in a polyhedral domain (1987)
    Springer
    Probability theory and related fields 75 (1987), S. 459-485 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper is concerned with the characterization and invariant measures of certain reflected Brownian motions (RBM's) in polyhedral domains. The kind of RBM studied here behaves like d-dimensional Brownian motion with constant drift μ in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit. Under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in Harrison-Williams [9], it is shown that such an RBM can be characterized in terms of a family of submartingales and that it reaches non-smooth parts of the boundary with probability zero. In [9], a purely analytic problem associated with such an RBM was solved. Here the exponential form solution obtained in [9] is shown to be the density of an invariant measure for the RBM. Furthermore, if the density is integrable over the polyhedral state space, then it yields the unique stationary distribution for the RBM. In the proofs of these results, a key role is played by a dual process for the RBM and by results in [9] for reflected Brownian motions on smooth approximating domains.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00320328
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  • 7
    Digitale Medien
    Digitale Medien
    A boundary property of semimartingale reflecting Brownian motions (1988)
    Springer
    Probability theory and related fields 77 (1988), S. 87-97 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We consider a class of reflecting Brownian motions on the non-negative orthant inR K . In the interior of the orthant, such a process behaves like Brownian motion with a constant covariance matrix and drift vector. At each of the (K-1)-dimensional faces that form the boundary of the orthant, the process reflects instantaneously in a direction that is constant over the face. We give a necessary condition for the process to have a certain semimartingale decomposition, and then show that the boundary processes appearing in this decomposition do not charge the set of times that the process is at the intersection of two or more faces. This boundary property plays an essential role in the derivation (performed in a separate work) of an analytical characterization of the stationary distributions of such semimartingale reflecting Brownian motions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01848132
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  • 8
    Digitale Medien
    Digitale Medien
    Reflected brownian motion in a wedge: Semimartingale property (1985)
    Springer
    Probability theory and related fields 69 (1985), S. 161-176 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, the object of study is reflected Brownian motion in a two-dimensional wedge with constant direction of reflection on each side of the wedge. The basic question considered here is “When is this process a semimartingale?”. It is first shown that a related process, defined by specifying the corner of the wedge to be an absorbing state, rather than an instantaneous one, is a semimartingale. Conditions for the existence and uniqueness of the process for which the corner is an instantaneous state were given by Vardhan and Williams (“Brownian motion in a wedge with oblique reflection”, Comm. Pure Appl. Math., to appear). Under these conditions, it is shown that starting away from the corner, the process is a semimartingale if and only if there is a convex combination of the directions of reflection that points into the wedge. This equivalence is also shown to hold starting from the corner, except in one unresolved case for which the wedge angle exceeds π and the directions of reflection are exactly opposed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02450279
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  • 9
    Digitale Medien
    Digitale Medien
    Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant (1993)
    Springer
    Probability theory and related fields 96 (1993), S. 283-317 
    Details
    ISSN: 1432-2064
    Schlagwort(e): 60J60 ; 60J65 ; 60G44 ; 60K25 ; 58G32
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ℝ d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this “pushing” at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01292674
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  • 10
    Digitale Medien
    Digitale Medien
    Correction to: A boundary property of semimartingale reflecting brownian motions (1989)
    Springer
    Probability theory and related fields 80 (1989), S. 633-633 
    Details
    ISSN: 1432-2064
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00318910
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