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  • 1
    Electronic Resource
    Electronic Resource
    A Bayes-optimal sequence-structure theory that unifies protein sequence-structure recognition and alignment (1998)
    Springer
    Bulletin of mathematical biology 60 (1998), S. 1039-1071 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract A rigorous Bayesian analysis is presented that unifies protein sequence-structure alignment and recognition. Given a sequence, explicit formulae are derived to select (1) its globally most probable core structure from a structure library; (2) its globally most probable alignment to a given core structure; (3) its most probable joint core structure and alignment chosen globally across the entire library; and (4) its most probable individual segments, secondary structure, and super-secondary structures across the entire library. The computations involved are NP-hard in the general case (3D-3D). Fast exact recursions for the restricted sequence singleton-only (1D-3D) case are given. Conclusions include: (a) the most probable joint core structure and alignment is not necessarily the most probable alignment of the most probable core structure, but rather maximizes the product of core and alignment probabilities; (b) use of a sequence-independent linear or affine gap penalty may result in the highest-probability threading not having the lowest score; (c) selecting the most probable core structure from the library (core structure selection or fold recognition only) involves comparing probabilities summed over all possible alignments of the sequence to the core, and not comparing individual optimal (or near-optimal) sequence-structure alignments; and (d) assuming uninformative priors, core structure selection is equivalent to comparing the ratio of two global means.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1006/S0092-8240(98)90002-7
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  • 2
    Electronic Resource
    Electronic Resource
    On a linear model of mechanical phase transitions (1990)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 728-733 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Existence and infinite speed of propagation are shown for the equation $$h_n \left( {x,t} \right) = \frac{1}{{\alpha \pi }}\int_{ - \infty }^\infty {\frac{{Ah_{xxx} \left( {\xi ,t} \right) - Bh_{xt} \left( {\xi ,t} \right)}}{{\left( {x - \xi } \right)}}d\xi } , - \infty〈 x〈 \infty ,0〈 t〈 T,$$ which is the linearization of a model equation for the mechanical phase transition phenomenon of melting-freezing waves. In addition, from the formal solution of the equation one can compute a decay rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946104
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  • 3
    Electronic Resource
    Electronic Resource
    Derivation of linear beam equations using nonlinear continuum mechanics (1993)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 44 (1993), S. 732-754 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Familiar linear elastic and viscoelastic beam equations (Euler-Bernoulli, Rayleigh, Kelvin-Voigt, Timoshenko, and Shear Diffusion) and boundary conditions are derived from a nonlinear theory of large motions rather than the usual variational techniques. Also included is a fairly detailed derivation of the nonlinear theory and a careful discussion of the hypotheses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00948486
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  • 4
    Electronic Resource
    Electronic Resource
    Book reviews (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 999-1002 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00920047
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  • 5
    Electronic Resource
    Electronic Resource
    Steady-state problems of nonlinear electro-magneto-thermo-elasticity (1986)
    Springer
    Archive for rational mechanics and analysis 95 (1986), S. 279-323 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276839
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  • 6
    Electronic Resource
    Electronic Resource
    Phase transitions and hysteresis in nonlocal and order-parameter models (1995)
    Springer
    Meccanica 30 (1995), S. 541-565 
    Details
    ISSN: 1572-9648
    Keywords: Phase transitions ; Hysteresis ; Order-parameter ; Nonlocal equations ; Phase transformations ; Solid mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Il lavoro descrive due tipi di regolarizzazione del problema quasistatico per un potenziale con due minimi in una dimensione. Un modello evidenzia caratteri di non località spaziale, mentre l'altro conduce ad una teoria con parametro d'ordine. Si derivano alcuni risultati di esistenza e regolarità e si presentano alcuni studi numerici che mostrano l'isteresi e il moto delle frontiere tra le fasi.
    Notes: Abstract The paper describes two types of regularization to the basic quasistatic double-well potential problem in one space dimension. One model features a spatially nonlocal term while the other incorporates the use of an order parameter. Some basic existence and regularity results for these modified models are derived and some numerical calculations that show hysteresis and motion of phase boundaries are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01557084
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  • 7
    Electronic Resource
    Electronic Resource
    Nonlocal regularization of L. C. Young's tacking problem (1992)
    Springer
    Applied mathematics & optimization 25 (1992), S. 287-301 
    Details
    ISSN: 1432-0606
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract L. C. Young's tacking problem is a prototype of a nonconvex variational problem for which minimizing sequences for the energy do not attain a minimum. The “minimizer” of the energy is usually described as a Young-measure or generalized curve. In many studies, the tacking problem is regularized by adding a higher-order “viscosity term” to the energy. This regularized energy has classical minimizers. In this paper we regularize instead with a spatially nonlocal term. This weakly regularized problem still has measure-valued minimizers, but as the nonlocal term becomes stronger, the measure-valued solutions organize, coalesce, and eventually turn into classical solutions. The information on the measure-valued solutions is obtained by studying equivalent variational problems involving moments of the measures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182325
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  • 8
    Electronic Resource
    Electronic Resource
    Nonlocal superconductivity (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 135-152 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00942851
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  • 9
    Electronic Resource
    Electronic Resource
    Some remarks on nonlocal interactions and hysteresis in phase transitions (1994)
    Springer
    Continuum mechanics and thermodynamics 8 (1994), S. 65-73 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper examines models of shape memory alloys in which the usual multiwell, nonconvex elastic energy is modified by the addition of a nonlocal interaction term. It is shown that minimizing such an energy over uniform Young-measures yields a good prediction of hysteresis in a material subjected to biaxial loading. In addition, the relationship between the nonlocal interaction energy and the coherency energy is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175752
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  • 10
    Electronic Resource
    Electronic Resource
    Original Article Some remarks on nonlocal interactions and hysteresis in phase transitions (1996)
    Springer
    Continuum mechanics and thermodynamics 8 (1996), S. 65-73 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: This paper examines models of shape memory alloys in which the usual multiwell, nonconvex elastic energy is modified by the addition of a nonlocal interaction term. It is shown that minimizing such an energy over uniform Young-measures yields a good prediction of hysteresis in a material subjected to biaxial loading. In addition, the relationship between the nonlocal interaction energy and the coherency energy is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175752
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