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  • 1
    Digitale Medien
    Digitale Medien
    Explicit periodic trend of van der Waals radii (1992)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 96 (1992), S. 9194-9197 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j100202a023
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  • 2
    Digitale Medien
    Digitale Medien
    Algebra of stereogenic pairing equilibria. 1. General model. 2. Stereoselective reactions under thermodynamic control (1992)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 96 (1992), S. 4701-4706 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j100190a102
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  • 3
    Digitale Medien
    Digitale Medien
    Algebra of stereogenic pairing equilibria. 3. Chiral discrimination (1992)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 96 (1992), S. 4706-4711 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j100190a103
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  • 4
    Digitale Medien
    Digitale Medien
    Chemical algebra. I: Fuzzy subgroups (1994)
    Springer
    Journal of mathematical chemistry 16 (1994), S. 245-256 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract Using the notion of fuzzy subset, the algebraic formulation of the constant of stereogenic pairing equilibria between skeletal analogs (previously disclosed) is connected to symmetry group theory. A distinction is introduced between geometrical (skeletal) symmetry and topographical (numerical parameters) symmetry. In order to describe “topographical symmetry”, a formal extended definition of a subgroup is proposed. Fuzzy subsets of the skeletal groupG are endowded with a structure which can be defined without referring to the geometrical representation of the abstract group isomorphic toG. The relevance of these propositions is evidenced by their “integer interpretation” meeting basic definitions of group theory, as well as by their role in expressing chemical pairing constants.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169211
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  • 5
    Digitale Medien
    Digitale Medien
    Chemical algebra. IV: “Length” of transformation pathways between skeletal analogs (1994)
    Springer
    Journal of mathematical chemistry 16 (1994), S. 285-308 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract Even if the eq. $$(\mathbb{E})$$ of completely G-invariant distance extensions derived from a pairing product is not resolved, a distance is defined by means of a metric obtained by differential resolution. Under specified conditions, the linear element solution do2 is homogeneous to square coordinate differentials. Integration of da along a curve of E affords a length relative to doe. Boundaries of the curve represent skeletal analogs u and v, whereas inner points represent intermediates in the transformation u → v, where the ligand parameters are supposed to vary continuously: a stereogenic pairing equilibrium between infinitesimally close skeletal analogs is assumed. If the curve runs orthogonal to a unit representation space of G, the length is infinite and the curve might be regarded as a “fractal” transformation pathway. The “thermodynamic gap” Dp is always shorter than the “kinetic” distance of the metric do2.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169214
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  • 6
    Digitale Medien
    Digitale Medien
    Chemical algebra III: Thermochemical approach to completely G-invariant distances (1994)
    Springer
    Journal of mathematical chemistry 16 (1994), S. 269-283 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The search for a definition of distances over sets of skeletal analogs (identified to G-Hilbert spaces of vector ligand parameters) is initiated from the algebraic formulation of the constant of stereogenic pairing equilibria (pairing product). A basic definition equation is devised from thermodynamical speculations. The equation is proved to have always a single potential distance solution Dp as soon as the pairing product is discriminating. The equation of Dp is constructed in order to satisfy three consistency requirements: completeG-invariance (arbitrary orientations selected to describe skeletal analogs do not affect the value of Dp); extension properties (Dp coincides with two standard completelyG-invariant distances or with the Euclidean distance in borderline cases); all the distance properties except, perhaps, the triangular inequality. The latter point remains challenging in general, and is computationally verified in some examples.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169213
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  • 7
    Digitale Medien
    Digitale Medien
    Chemical algebra. II: Discriminating pairing products (1994)
    Springer
    Journal of mathematical chemistry 16 (1994), S. 257-268 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The algebra of stereogenic pairing equlibria is presented in a very general context. Starting from the notions of fuzzy subgroup and conjugacy link, chemical pairing constants between molecular speciesu andv having a skeletal symmetry groupG are formulated as “pairing products” on aG-Hilbert space. “Discriminating pairing products”K are defined by the conditions: “K ⩾ 1” and “K = 1 → the representative vectors of the paired species areG-equivalent”. WhenG has only two elements, the pairing product is always discriminating. For several skeletal symmetries, if the vectors are “enantiomorphic (v = σu, σ2 =e, σ ≠G), thenK is greater than 1 and reaches 1 only ifu is “achiral”: “chirality indexes” and general “permutational indexes” are then defined fromK(u σu). The general model is illustrated by some examples.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01169212
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  • 8
    Digitale Medien
    Digitale Medien
    Chemical algebra. VII: ImproperG-weighted metrics of non-compact groups: Lorentz group in the Minkowski space (1995)
    Springer
    Journal of mathematical chemistry 17 (1995), S. 265-283 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The principles and the generalized equation of chemical algebra is extended to a Minkowskian substrateE endowed with its improper non-definite-positive metric, where the non-compact 6-parameter groupG of the Lorentz transformations operates. Given a map μu,u(g) = μ(gu)m(g) onG, a “line element”ds 2 is formulated at each point marked by a vectoru. Assuming “μ = 1” and “m(g) :≠ 0 ⇒g is a pure Lorentz transformation (without a spatial rotation)”, the isotropic hypothesis (m depends on a single parameter out of three inG) is first studied. In general,ds 2 does not define a Riemannian manifold unless one additional condition onm is imposed. Several relationships are established which are useful for the calculation of the metric tensor and the curvature tensor.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01164851
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  • 9
    Digitale Medien
    Digitale Medien
    Chemical algebra. VI:G-weighted metrics of non-compact groups: Group of translations in the Euclidean space (1995)
    Springer
    Journal of mathematical chemistry 17 (1995), S. 247-264 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The generalized definition equation of a G-weighted metricds 2 from the datum of any groupG acting onto a vector space mapped by a continuous numerical functionμ is applied whenE =R n andG = the group of translations inR n . Here,G does not act linearly inR n andR n is considered as an affine space. The solution readsds 2 = −d 2(InI)/(Bp),I = (4iπx 0) n/2 ·ψ, wherex 0 = −i/(2p), ψ is a solution of the Schrödinger-type equation Δψ +iϖψ/ϖx 0 = 0, andB is a uniform term depending onx 0. Whenn = 3,p is interpreted as the reciprocal of a time variable. Attempts to identifyds 2 with the spatial part of a space-time metric of general relativity failed except for the flat Robertson and Walker spaces. In the simplest case,B = 1/R 2(t) and $$\Psi (p,r) = e^{ - pr^2 /2}$$ . A uniform but non-constant “imaginary potential energy” of the space can be formally derived: V(x 0) = 3i/(2x 0). Despite a striking formal link with tools of physical mathematics, no physical validation of the propositions of chemical algebra is claimed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01164850
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  • 10
    Digitale Medien
    Digitale Medien
    Chemical algebra. V:G-weighted distance extensions and metrics (1995)
    Springer
    Journal of mathematical chemistry 17 (1995), S. 235-246 
    Details
    ISSN: 1572-8897
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: Abstract The first formulation of the definition equation of completely-G-invariant distance extensions from the action of a compact group G onto a metric space (E, d) is reminded. A more general equation ( $$\mathbb{E}$$ ) is then consistently associated to a group G mapped by a numerical functionm and acting on a metric space (E, d) mapped by another continuous numerical function. A solution of ( $$\mathbb{E}$$ ) is called a “G-weighted distance extension ofd”. A differential form of the equation is derived in order to provide a definition of a “G-weighted metric”ds 2 = (dσ/γ)2 from a non-uniform map of an Euclidean space:γ = #G whenG is a finite group, butds 2 is also defined by continuity whenG is an infinite compact group (γ = oo).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01164849
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