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91.
Íñigo X. García-Zubiri Gustavo González-Gaitano José Ramón Isasi 《Journal of inclusion phenomena and macrocyclic chemistry》2007,57(1-4):265-270
Automated semi-rigid docking has been explored as an alternative approach for the theoretical study of the inclusion complexes
with cyclodextrins. To this purpose we have chosen as a model for the binding to βCD some naphthalene derivatives (naphthalene,
2-ethylnaphthalene, 2-acetylnaphthalene, 1-naphthyl acetate, 2-naphthyl acetate and 1-naphthol). For comparison purposes,
the binding constants in water and the associated thermodynamic parameters have been obtained under the same experimental
conditions by steady-state fluorescence spectroscopy. The calculations of the automated docking regarding the topology of
the guest inside the cavity produce a cluster of structures that qualitatively agrees with fluorescence results and literature
data. However, the predicted values of the free energy of binding are lower than the experimental ones by ca. −10 kJ mol−1, and very close to the experimental enthalpy of binding deduced from the temperature dependence of the association constants.
The differences are ascribed mainly to the assumption of rigidity of the CD into the auto-docking scheme. 相似文献
92.
We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These
are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form,
whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through
the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present
as a case study of this approach, the invariant Navier–Stokes equations for viscous fluids, and the kinematic dynamo equation
of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between
them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random
extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional
almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and
the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing
polygonal smooth almost everywhere realizations of the random representations. 相似文献
93.
We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections
of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions
whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations,
characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that
generalizes the Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for
a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state
which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian
potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions
generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the
sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written
on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process
generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal
rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes
equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant
diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore,
the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian
motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and
Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate
the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form
of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field
equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that
the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between
an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when
we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss
the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted
to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to
include the electromagnetic potential terms of Q 相似文献
94.
The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of Thomas–Whitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an
-equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.Mathematics Subject Classification (2000). 53B05, 53B10, 53D50, 53C10 相似文献
95.
This paper deals with moduli spaces of framed principal bundles with connections with irregular singularities over a compact Riemann surface. These spaces have been constructed by Boalch by means of an infinite-dimensional symplectic reduction. It is proved that the symplectic structure induced from the Atiyah–Bott form agrees with the one given in terms of hypercohomology. The main results of this paper adapt work of Krichever and of Hurtubise to give an interpretation of some Hitchin Hamiltonians as yielding Hamiltonian vector fields on moduli spaces of irregular connections that arise from differences of isomonodromic flows defined in two different ways. This relies on a realization of open sets in the moduli space of bundles as arising via Hecke modification of a fixed bundle. 相似文献
96.
We show that the Chern–Simons theory for a principal G-bundle P over a three-dimensional manifold, with G an arbitrary Lie group, can be formulated as a variational problem defined by local data on the bundle of connections C(P) of P. By means of the theory of variational problems defined by local data we prove that the Euler–Lagrange operator and the differential of the Poincaré–Cartan form can be intrinsically expressed in terms of the symplectic form and the curvature morphism of C(P). These facts and the theory of the global inverse problem of the Calculus of Variations allow us to prove that there is indeed a global Lagrangian density for these theories. We also prove that every infinitesimal automorphism of P produces in a natural way an infinitesimal symmetry of the variational problem defined by the Chern–Simons theory. We therefore conclude that the algebra of infinitesimal symmetries of these theories is infinite dimensional. 相似文献
97.
Srichan Arworn 《Southeast Asian Bulletin of Mathematics》2001,25(2):191-200
To characterize all complete sublattices of a given complete lattice is an important problem. In this paper we will give three different characterizations of complete sublattices of a complete lattice by using closure operators, kernel operators, and by using Galoisclosed subrelations.The research was supported by a grant of the faculty of Science ChiangMai University Thailand. 相似文献
98.
Lutz Habermann 《Annals of Global Analysis and Geometry》1993,11(4):311-322
TheL
2-metric {ie311-1} on the moduli spaceM
1(Q) of self-dualSU(2)-connections with instanton number 1 over the Euclidean 4-space is described. It is shown that the Riemannian manifold (M
1(Q), {ie311-2}) is isometric to R+ × R4 with the Euclidean metric.Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 288 相似文献
99.
There exists an Ehresmann connection on the fibred constrained sub-manifold defined by Pfaffian differential constraints.
It is proved that curvature of the connection is closely related to the d-σ commutation relation in the classical nonholonomic
mechanics. It is also proved that conditions of complete integrability for Pfaffian systems in Frobenius sense are equivalent
to the three requirements upon the conditional variations in the classical calculus of variations: (1) the variations belong
to the constrained manifold, (2) variational operators commute with differential operators, (3) variations satisfy the Chetaev's
conditions. Thus this theory verifies the conjecture or experience of researchers of mechanics on the integrability conditions
in terms of variation calculus.
The project supported by the National Natural Science Foundation of China 相似文献
100.
H. Figueroa J. M. Gracia-Bondí a F. Lizzi J. C. V rilly 《Journal of Geometry and Physics》1998,26(3-4):329-339
Using the formalism of superconnections, we show the existence of a bosonic action functional for the standard K-cycle in noncommutative geometry, giving rise, through the spectral action principle, only to the Einstein gravity and Standard Model Yang-Mills-Higgs terms. 相似文献