| 词汇 | example_english_symmetry |
| 释义 | Examples of symmetryThese examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. The last three categorical axioms are concerned with symmetries. In particular the auxiliary tiles needed in all such formats can be characterized as the bidimensional counterparts of symmetries, duplicators and dischargers. Because an equivalence is reflexive, they include all original symmetries. The following representation theorem states the correspondence between double symmetries and ordinary symmetries. The helical symmetries of these filaments are the same irrespective of the original flagellin species. The notion of symmetries plays a key role for the establishment of the result. Here we study some of their basic properties, such as metric properties, symmetries, and spectral properties. Nonlinearizable holomorphic dynamics having an uncountable number of symmetries. We turn now to continuous translation symmetries, which do not have analogues in crystal structure. We first describe the computational results and then discuss the symmetries of the numerical solutions in order to establish the underlying bifurcation structure. Correspondingly, these symmetries imply the conservation laws of momentum and angular momentum. Furthermore, rules representing symmetries can be automatically detected using the modified algorithm. Examples of such features are symplecticity, volume preservation, integrals, symmetries, and many more. The other 40 matrices, which involve nontrivial permutations of the a(1) subalgebras, do not generate symmetries of the system. The par t rotational symmetries are measured with respect to the par t inser tion axis and an axis perpendicular to the inser tion axis. To summarise, the fourth method gives shorter, more manageable conditions which, strictly speaking, do not compute conservation laws but adjoined symmetries. The adjoint symmetries satisfy a linear determining equation that is the adjoint of the determining equation for symmetries. Substituting the solution into the original (nonlinear) determining equations, and then factoring out the known continuous symmetries, produces a list of all discrete point symmetries. By solving (2.9) and checking to see which of the solutions are symmetries, we obtain the following result. In $4 we discuss techniques for finding and utilizing adjoint symmetries in conjunction with the adjoint-invariance condition. Application of a simple flaking procedure, without any image manipulation, could not have produced the kinds of three-dimensional symmetries evident on these artifacts. Unlike his suggestion, this traditional definition and the recent holographic definition are relevant to the discussion on the cognitive evolution of visual symmetries. Generating lines guided the design decisions and dimensions, creating symmetries, which were sometimes disguised by a layering of elements. Analogously, regular asymptotic solutions can be found in higher approximations and for other symmetries. The smallest portion of structural information required to reconstruct the entire lattice through crystallographic symmetries and lattice translations is termed the asymmetric unit. Identifying biological dimers is particularly difficult, as crystallographic symmetries tend to generate many dimeric interactions. We can then instantiate this notion of generalized natural transformation to deal with symmetries, duplicators, and dischargers as special instances of the general notion. An attempt to clarify the form by segmenting it and by introducing spatial symmetries helps to introduce order into this work. We can note, however, that similar techniques are useful for both approaches: removing symmetries and adding cuts (redundant constraints) greatly improve the running times. Horizontal symmetries are not needed in this case, because the vertical symmetries are expressive enough to represent all the possible communications. Example 2.11), has the full symmetries; for the others we assume only trivial symmetries (that is, the identities). Equations were represented as vectors of parameters (seen as elements of an inductive type) and the group itself as symmetries acting on coefficients. More precisely, if we omit that axiom, we can find some object u such that the group of symmetries on u has infinite order. Second, there is the group of spatiotemporal symmetries defined in the following way. Such a coincidence might not be surprising, as all of them share the same type of symmetries. Consequently, in practice one must resort to specific ansatze in order to find adjoint symmetries. An object possessing one or more symmetries entails a modification of the manifold of distinguishable positions. I do not, however, believe that this middle ground can adequately account for the three-dimensional, congruent symmetries of late handaxes. Apes do not produce symmetries naturally and have never been trained to do so. Here we can see possible symmetries as patterns of elements in a composition, not just inherent in a single object. I have dwelt at alarming length on tacit symmetries pointing to bodies under bodies. However, for discrete symmetries, no such linearization is possible. The new method presented in this paper can deal with a wide range of symmetries, both local and nonlocal. Having looked at symmetries, which entail the invariance of the fixed set fix h l o y ? With the exception of substitution decompositions, these techniques are not invariant under the eight permutation class symmetries. In particular, existing symbolic manipulation programs [8] that calculate symmetries can be readily adapted to calculate solutions of the conservation law determining system. In particular, the same algorithmic procedures which one uses to solve determining equations for symmetries can be used to solve the determining system for multipliers. To find a solvable structure of, say p, non-trivial symmetries, the above procedure must be carried out p times. Consequently, any two point symmetries can be obtained from each other through a point transformation. The first stage is to clarify the symmetries of the various patterns that are involved. There are several symmetries in the dynamical plane. We use the extensive symmetries of the figure-eight solution to reduce the stability calculations down to the behavior of the first twelfth of the orbit. Luckily, in many cases, natural splittings do preserve symmetries. The following example preserves phase space volume and has 8 discrete symmetries and 8 discrete reversing symmetries. Furthermore, the systems are subject to thermal motion which distort the imposed symmetries. There are three independent rotational i symmetries that span the rotation subalgebra obtained by setting i = k where k = 1, 2, 3, respectively. The above simple example illustrates how an infinite family of symmetries can be generated from two given symmetries. The changes of variables are chosen in such a way as to preserve certain symmetries. We shall explain how this naturally leads to the general concept of invariant cyclic cohomology in the framework of quantum group symmetries. Since the embeddings accompany base isomorphisms, we have that the free names and symmetries of a source process and its translation coincide. In the above definition, assigns the necessary symmetries on the resulting quotient. The following results show that symmetries also give basic insights into the algebraic constructions we have already presented. However, the two possible generalized symmetries are shown to be equivalent (the reason is that symmetries are isomorphisms). Again, we work with states that are strings instead of multisets, as the symmetries introduce all the possible rearrang ements. The group of automorphisms of a graph characterizes its symmetries and are therefore very useful for determining some of its properties. The cue here is taken from what field theorists have come to call the gauge principle or principle of local symmetries. The images correspond to a real, complex environment, with symmetries in the scene, light reflection and moving objects, such as people. By starting from random walks produced by stochastic functions, and by injecting symmetries, regularities and periodicities, even up to the point of repeated waveforms. In particular, we show how to utilize known first integrals and symmetries to find new integrating factors. Unfortunately given incorrect symmetries ab-initio programs will often find shapes that also fit the scattering profiles. What selective advantage could congruency, three-dimensional symmetries, and image manipulation bestow on a hunter-gatherer? In that case the conditions (4.5) have additional adjoined symmetries as solutions. Similarly, operators on triangular lattices lead to splittings with symmetries of order three. As a consequence some of the original symmetries disappear, and the resulting structure turns out to be more involved. After presenting the computational results we describe the symmetries of the numerical solutions and then establish the underlying bifurcation structure. We assume that the composed nets own symmetries induced by obvious geometric symmetries. Further, isomorphisms completely characterise symmetries in addition to free names. They do not tell the whole story about placing; the three categorical axioms for symmetries are important for the permutation of places. The following proposition is an easy consequence of the yanking and naturality conditions, keeping in mind functoriality of and naturality of symmetries. The efficiency of his prose rests on the organisation of images which follow a pattern of symmetries and repetitions. The self-absorption effects in homogeneous plasmas are modeled using the escape factor formalism for planar, cylindrical, and spherical symmetries. Succinctly, the connection is this : conservation laws are implications of symmetries embodied in dynamical laws. Imposing higher symmetries resulted in noticeably higher x2 values and marginally poorer fits to the data. In contrast, symmetries that do not apply to the lattice are non-crystallographic. If these symmetries apply to the entire lattice, they are crystallographic symmetries and constrain the parameters of the unit cell. Further improvements in the analysis phase are possible, such as better discovery of symmetries (implied from rules) and improved continuation optimization. The discovery of functional dependencies, set semantics and symmetries is generally very cheap since only a linear pass over the program is required. We also work out the explicit form of our condition for the dihedral group of symmetries of a regular polygon. In situations where a significant proportion of the structures have no nontrivial symmetries, it is already fairly well understood how to apply this tool. In that application, the symmetries are such that the coefficient c0 = 0 in equation. The method of equivariant bifurcation theory is generally applicable to the minimisation of functions with symmetries. However, all symmetries of a differential equation do not necessarily arise from symmetries of the action when there is a variational principle. We also give a criterion for outerness of such automorphisms, including the group of symmetries of a regular icosahedron. Our definitions are inclusive and allow sets with translation symmetries. Here we shall restrict ourselves to linear and affine symmetries. The production of symmetries, on the other hand, requires the use of an asymmetrically organized cognitive system and asymmetrical use of bimanual coordination. The rhythm of the gates provides the key to the dynamic symmetries of the house. Nevertheless, global instabilities are as physical as local instabilities, at least in finite containers where finite symmetries are usually present. Spatial symmetries introduce a degree of formal organisation. The heteropolymeric nature of proteins introduces effective defects into the structure, making the symmetries approximate. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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