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  • 1
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 39-48 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The relations between the general form of Carbó's quantum similarity measure and the similarity measure based on the Löwdin transform of approximate density matrices are discussed. These relations provide the basis for the study of macromolecular forces and small deformations of electron densities induced by limited changes of nuclear configurations of both small and large molecules. © 1997 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 63 (1997), S. 105-109 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The scaling-nesting similarity measures were proposed earlier for an intuitively simple shape comparison of molecular “bodies” enclosed by isodensity surfaces. Similarity measures have extended utility and provide rigorous comparisons which can be treated by well-known mathematical techniques if they fulfill the conditions for a metric. Here, a proof is presented showing that the symmetric scaling-nesting dissimilarity measure is indeed a proper metric. Some additional features, relevant to the newly proven properties of these similarity measures, are discussed. © 1997 John Wiley & Sons, Inc.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 64 (1997), S. 669-678 
    ISSN: 0020-7608
    Keywords: Molecular geometry ; symmetry ; symmorphy ; topology ; electron density ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Relations between an earlier generalization of molecular symmetry called symmorphy and a molecular equivalence based on diffeomorphisms of electron density functional graphs (the so-called DFG equivalence introduced in our previous work) are analyzed. Any two DFG-equivalent electron density functions can be derived from one another by a suitable transformation of the spatial coordinates and the electronic charge density scale; the classes of DFG equivalence are the orbits of a group of linear operators operating in the space of electron density functions. Within the symmorphy framework, the symmetry group is derived from the symmorphy group by taking an intersection of a subgroup of the symmorphy group and the group of isometries for a natural choice of the Riemannian metric tensor. The Riemannian metric properties provide a choice for a suitable reference electron density function for each class of equivalent densities. Such reference densities serve as tools for a systematic classification of the infinite family of electron densities of molecular conformations.   © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 669-678, 1997
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 99-105 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The distribution of the essential functional groups within biomolecules is described by a series of polyhedral models. As a function of a threshold of the electronic density of the biomolecule, the combinatorial types of these polyhedra are threshold-dependent within each series, resulting in a characteristic sequence of combinatorial types for each biomolecule. A comparison of combinatorial types is the basis for the introduction of new measures of shape similarity and shape complementarity between biomolecules.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 99-105, 1998
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 0020-7608
    Keywords: linear operator ; *-algebra ; general topology ; asymptotic analysis ; chemical network systems ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Part IV of this series consists of two complementary subparts devoted to attain the following two goals: (i) By shifting from the previous setting of the Banach algebra B(B)=B(B, B) to a broader setting of the space B(X, B) of all bounded linear operators from a normed space X to a Banach space B, we extend our previous theoretical framework to incorporate part of the theory of additive correlation involving the Asymptotic Linearity Theorems, which have been developed for a study of correlation between structure and properties in molecules having many identical moieties, especially in macromolecules having repeating units. (ii) By reverting our focus to the special algebra B(H) with H being a Hilbert space, we develop a theorem which is useful for a structural analysis of spectral symmetry of linear operators representing physico-chemical network systems.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 57-69, 1998
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 353-361 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A family of related techniques for the reduction of square-cell configurations (“animals”) to simpler ones by cell-shedding processes provide physically motivated, novel approaches for shape characterization and similarity criteria as well as similarity measures based on equivalence relations. The two main algorithms, csk, k = 1, 2, involve the simultaneous “shedding” of all cells having precisely k sides exposed on the periphery of the animal; the shedding steps are repeated as long as the resulting structure is an animal. Since the termination criteria of these two algorithms are different, they can be combined sequentially into composite algorithms, leading to various alternative shape characterizations and equivalence relations. The third main algorithm, cs32, involves incomplete elimination of peripheral cells of a given type, thus retaining some additional local shape features inherited from the original animal. Following the introduction of these transformations, some of their properties are derived and several examples are discussed. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 353-361, 1997
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 0020-7608
    Keywords: linear operator ; banach algebra ; general topology ; asymptotic analysis ; chemical network systems ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: By extending the methodology given in Parts I and II of this series of articles, certain dynamical systems of chemical kinetic equations are analyzed in the setting of the Banach algebra B(B) of all bounded operators acting on a Banach space B. In this article, we proceed from the general setting of B(B), which played a central role in Part II, toward its specific application to the dynamical systems. In our analysis, crucial initial steps are taken by (i) equipping the abstract space B with the “positive quadrant,” which we denote by Γ(∝+n), and by (ii) investigating the asymptotic behavior of the solution χε(t) of the initial-value problem $dx(t)/dt = Tx(t), x(0)=\xi \in \Gamma(R^{+n})\subset {\cal B} \hbox{, where } T \in {\bf B}({\cal B})$ is suitably specified for our application purposes. The main theorem and its two specialized versions, together with the notions of Γ-semipositive operators and semipositive matrices presented here, serve as fundamental tools for the analysis of a class of dynamical systems of chemical kinetic equations whose examples were illustratively treated in the previous parts of this series of articles. The techniques developed here for an asymptotic analysis of chemical kinetic dynamical systems will be linked and unified with those for the asymptotic analysis of quantum mechanical systems in a forthcoming part of this series of articles. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 149-163, 1997
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 1337-1344 
    ISSN: 0192-8651
    Keywords: density averaging ; average conformation ; molecular deformations ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: The concepts of averaged electron densities and averaged nuclear arrangements are discussed with reference to small nuclear distortions and an electron density transformation based on the inverse Löwdin transform.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 1337-1344, 1998
    Type of Medium: Electronic Resource
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