Global invariance properties

Also global fitting techniques, where the space invariance (or any other invariance property) of one or more fitting parameters is exploited, have been successfully used to analyze fluorescence lifetime images [45, 46]. When applicable, global analysis techniques provide more homogeneous SNRs and reduce the number of fitted parameters. 

Healey G and Slater D 1994 Global color constancy recognition of objects by use of illumination-invariant properties of color distributions. Journal of the Optical Society of America 11(11), 3003-3010. 

A practical implementation of the above approach is the following a global shape property of the molecule is assigned to each point of the sphere S, followed by the determination of those domains of S where this shape property is invariant. A pair of examples is shown in Figure 5.9, where the shape globe invariance domains of a MIDCO surface for two relative convexity shape domain partitionings (P) with respect to two reference curvatures, b = 0, and b < 0, are given. As... 

Conformational-Dependent Chirality Code chirality descriptors (0 Chirality Codes) conformational global sensitivity molecular descriptors (0 invariance properties of... 

Alignment independent descriptors can be derived from the molecular formula, from the 2D molecular graph, or from a 3D conformation. They cover global molecular properties, but also 3D chemical information at the molecular surface as provided, for instance, by the Molecular Surface Weighted Holistic Invariant Molecular descriptors (MS-WHIM) [52,53]. The class of alignment independent descriptors includes also properties which are obtained from QM calculations, such as dipole moment or orbital energies. 

In two-dimensional mappings, a global invariant set with a positive area is preserved by the escape dynamics. However, in four-dimensional mappings Arnold diffusion precludes the existence of complete barriers formed by invariant tori. Accordingly, no invariant set of positive Legesgue measure is expected to exist. Nevertheless, numerical integration shows that a quasi-invariant set persists for a very long time. This quasi-invariant set shows a property similar to the invariant... 

In a first step we will analyze the dominant condensation pattern in the scalar color antitriplet channel for a two-flavor system, i.e., we will consider the limit Ms —> 00. Looking at the transformation properties of the condensate S22 we can classify the symmetries of the 2SC phase. It is invariant under a global //(l)-symmetry generated by... 

The latter condition is commonly known as microscopic reversibility or local detailed balance. This property is equivalent to time reversal invariance in deterministic (e.g., thermostatted) dynamics. Although it can be relaxed by requiring just global (rather than detailed) balance, it is physically natural to think of equilibrium as a local property. Microscopic reversibility, a common assumption in nonequilibrium statistical mechanics, is the crucial ingredient in the present derivation. 

Maxwell theory, soliton flows are Hamiltonian flows. Such Hamiltonian functions define symplectic structures6 for which there is an absence of local invariants but an infinite-dimensional group of diffeomorphisms which preserve global properties. In the case of solitons, the global properties are those permitting the matching of the nonlinear and dispersive characteristics of the medium through which the wave moves. 

In Table 4 we summarize some global properties of the obtained JT minima for all charge and spin states. In these multi-mode JT systems, the local symmetry of an optimal distortion is described in terms of the subgroup GiOCai of symmetry operations which leave that minimum invariant. We remind that the minima in the... 

Due to the relative character of the number operator — /S/S0, all the physical predictions of the Floquent model must be invariant with respect to a global translation of the relative photon numbers. We show that this is indeed the case for the properties discussed above. The propability P(L, t) is independent of the particular initial photon number state chosen that is, it is independent of k since... 

The second symmetry requirement that the expression for the inter-molecular potential has to meet is that it must be invariant under any rotation of the global coordinate frame. The transformation properties of the symmetry-adapted functions Gj Hw) under such a rotation are easily obtained from Eqs. (10) and (5) ... 

The formal presentation of the problem was an attempt to develop a qualitative quantum-chemical model of the elementary polymerization act - adequately describing the complex of available experimental facts taking into account the above properties of propagation, the theoretical achievements of organic chemistry and the known principles of invariance in the framework of the axiomatic approach on the ideological basis of symmetry concepts. It should be emphasized that we do not mean to achieve in the present work a global interpretation of the entire experimental material accumulated in the literature. The aim of the author is mainly to demonstrate the promising character of this approach as a whole. 

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