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11.
Carlos Kozameh Ezra T. Newman Gilberto Silva-Ortigoza 《General Relativity and Gravitation》2008,40(10):2043-2050
A problem in general relativity is how to extract physical information from solutions to the Einstein equations. Most often
information is found from special conditions, e.g., special vector fields, symmetries or approximate symmetries. Our concern
is with asymptotically flat space–times with approximate symmetry: the BMS group. For these spaces the Bondi four-momentum
vector and its evolution, found at infinity, describes the total energy–momentum and the energy–momentum radiated. By generalizing
the simple idea of the transformation of (electromagnetic) dipoles under a translation, we define (analogous to center of
charge) the center of mass for asymptotically flat Einstein–Maxwell fields. This gives kinematical meaning to the Bondi four-momentum,
i.e., the four-momentum and its evolution which is described in terms of a center of mass position vector, its velocity and
spin-vector. From dynamical arguments, a unique (for our approximation) total angular momentum and evolution equation in the
form of a conservation law is found.
Third Award in the 2008 Essay Competition of the Gravity Research Foundation. 相似文献
12.
Gregory S. Ezra 《Journal of mathematical chemistry》2002,32(4):339-360
The theory of differential forms and time-dependent vector fields on manifolds is applied to formulate response theory for non-Hamiltonian systems. This approach is manifestly coordinate-free, and provides a transparent derivation of the response of a thermostatted system to a time-dependent perturbation. 相似文献
13.
On the performance of the ICP algorithm 总被引:2,自引:0,他引:2
We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay as a successful heuristic for matching of point sets in d-space under translation, but so far it seems not to have been rigorously analyzed. We consider two standard measures of resemblance that the algorithm attempts to optimize: The RMS (root mean squared distance) and the (one-sided) Hausdorff distance. We show that in both cases the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, under the RMS measure, for which we present a lower bound construction of Ω(nlogn) iterations, where n is the overall size of the input. Under the Hausdorff measure, this bound is only O(n) for input point sets whose spread is polynomial in n, and this is tight in the worst case.We also present several structural geometric properties of the algorithm under both measures. For the RMS measure, we show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector Δt of the relative translation. As a result, we conclude that the polygonal path π, obtained by concatenating all the relative translations that are computed during the execution of the algorithm, does not intersect itself. In particular, in the one-dimensional problem all the relative translations of the ICP algorithm are in the same (left or right) direction. For the Hausdorff measure, some of these properties continue to hold (such as monotonicity in one dimension), whereas others do not. 相似文献
14.
Zaleski CM Tricard S Depperman EC Wernsdorfer W Mallah T Kirk ML Pecoraro VL 《Inorganic chemistry》2011,50(22):11348-11352
The magnetic behavior of the pentanuclear complex of formula Mn(II)(O(2)CCH(3))(2)[12-MC(Mn(III)(N)shi)-4](DMF)(6), 1, was investigated using magnetization and magnetic susceptibility measurements both in the solid state and in solution. Complex 1 has a nearly planar structure, made of a central Mn(II) ion surrounded by four peripheral Mn(III) ions. Solid state variable-field dc magnetic susceptibility experiments demonstrate that 1 possesses a low value for the total spin in the ground state; fitting appropriate expressions to the data results in antiferromangetic coupling both between the peripheral Mn(III) ions (J = -6.3 cm(-1)) and between the central Mn(II) ion and the Mn(III) ones (J' = -4.2 cm(-1)). In order to obtain a reasonable fit, a relatively large single ion magnetic anisotropy (D) value of 1 cm(-1) was necessary for the central Mn(II) ion. The single crystal magnetization measurements using a microsquid array display a very slight opening of the hysteresis loop but only at a very low temperature (0.04 K), which is in line with the ac susceptibility data where a slow relaxation of the magnetization occurs just around 2 K. In frozen solution, complex 1 displays a frequency dependent ac magnetic susceptibility signal with an energy barrier to magnetization reorientation (E) and relaxation time at an infinite temperature (τ(o)) of 14.7 cm(-1) and 1.4 × 10(-7) s, respectively, demonstrating the single molecule magnetic behavior in solution. 相似文献
15.
16.
The translational absorption spectra of HeAr and NeAr have been analyzed with a hard-sphere potential to obtain the explicit dependence of the interaction dipoles on interatomic distance. The dipoles were found to consist of a short-range part varying almost exponentially with the distance and of a long-range part which varies more slowly. μHe Ar(r) exhibited an unexpected maximum at small distances. 相似文献
17.
A sufficient condition is given for a planar graph to be 4-colorable. This condition is in terms of the sums of the degrees
of a subset of the vertex set of the graph. 相似文献
18.
R. O. Hansen Allen I. Janis Ezra T. Newman John R. Porter Jeffrey Winicour 《General Relativity and Gravitation》1976,7(8):687-693
A representation of tensors and spinors at a point of space-time as spin and conformally weighted functions on the unit sphere is derived. Methods for performing algebraic operations on tensors and spinors in this representation are discussed.Supported in part by grants Nos. GP-35773X1 and MPS74-18020 from the National Science Foundation. 相似文献
19.
Laura Felicia Matusevich Ezra Miller 《Proceedings of the American Mathematical Society》2006,134(5):1375-1381
Let be an integer matrix, and assume that the convex hull of its columns is a simplex of dimension not containing the origin. It is known that the semigroup ring is Cohen-Macaulay if and only if the rank of the GKZ hypergeometric system equals the normalized volume of for all complex parameters (Saito, 2002). Our refinement here shows that has rank strictly larger than the volume of if and only if lies in the Zariski closure (in ) of all -graded degrees where the local cohomology is nonzero. We conjecture that the same statement holds even when is not a simplex.
20.
Kirk ML Shultz DA Depperman EC Brannen CL 《Journal of the American Chemical Society》2007,129(7):1937-1943
A Valence Bond Configuration Interaction (VBCI) model is used to relate the intraligand magnetic exchange interaction (J) to the electronic coupling matrix element (HAB) in Tp(Cum,MeZn)(SQNN), a compound that possesses a Donor-Acceptor (D-A) SemiQuinone-NitronylNitroxide (SQNN) biradical ligand. Within this framework, an SQ --> NN charge transfer state mixes with the ground state and stabilizes the spin triplet (S = 1). This charge-transfer transition is observed spectroscopically and probed using resonance Raman spectroscopy. In addition, the temperature-dependent electronic absorption spectrum of the Ni(II) complex, Tp(Cum,MeNi)(SQNN), has been studied. Exchange coupling between the S = 1 Ni(II) ion and S = 1 SQNN provides a mechanism for observing the formally spin-forbidden, ligand-based 3GC --> 1CTC transition. This provides a means of determining U, the mean GC --> CTC energy, and a one-center exchange integral, K(0). The experimental determination of J, U, and K(0) permits facile calculation of HAB, and we show that this methodology can be extended to determine the electronic coupling matrix element in related SQ-Bridge-NN molecules. As magnetic susceptibility measurements are easily acquired in the solid state, H(AB) may be effectively determined for single molecules in a known geometry, provided a crystal structure exists for the biradical complex. Thus, SQ-Bridge-NN molecules possess considerable potential for probing both geometric and electronic structure contributions to the magnitude of the electronic coupling matrix element associated with a given bridge fragment. 相似文献