The orbit of a point x in X is the set of elements of X to which x can be moved by the elements of G. The orbit of x is denoted by Gx: The orbits are {0,10,20}, {1,9,11,19,21,29}, {2,8,12,18,22,28}, {3,7,13,17,23,27}, {4,6,14,16,24,26}, and {5,15,25}. The points within an orbit are "equivalent". If a symmetry group applies for a pattern, then within each orbit the color is the same. The set of all orbits ...

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Dihedral group of order 6, Dihedral group of order 6 - Symmetry groups, Dihedral group of order 6 - Permutations of a set of three objects, Dihedral group of order 6 - Summary of group operations, Dihedral group of order 6 - Conjugacy classes, Dihedral group of order 6 - Subgroups, Dihedral group of order 6 - Semidirect products, Dihedral group of order 6 - Group action, Dihedral group of order 6 - Orbits and stabilizers, Dihedral group of order 6 - External link

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We can imagine "disturbing" the gravitational field outside some isolated massive object by "sending in some radiation from infinity". We can ask: what happens as the incoming radiation interacts with the ambient field? In the approach of classical perturbation theory, we can start with Minkowksi vacuum (or another very simple solution, such as the de Sitter lambdavacuum), introduce very small metric perturbations, and retain only terms up to some order in a suitable perturbation expansion-- somewhat like evaluating a kind of T ...

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Exact solutions in general relativity, Exact solutions in general relativity - Difficulties with the definition, Exact solutions in general relativity - Types of exact solution, Exact solutions in general relativity - Constructing solutions, Exact solutions in general relativity - Existence of solutions, Exact solutions in general relativity - Global stability theorems, Exact solutions in general relativity - The positive energy theorem, Exact solutions in general relativity - Examples

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Consider a group G acting on a set X. The orbit of a point x in X is the set of elements of X to which x can be moved by the elements of G. The orbit of x is denoted by Gx: Case that the group action is on R: For the trivial group, all orbits contain only one element; for a group of translations, an orbit is e.g. {..,-9,1,11,21,..}, for a reflection e.g. {2,4}, and for the symmetry group with translations and reflections e.g. {-8,-6 ...

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Symmetry groups in one dimension, Symmetry groups in one dimension - Translational symmetry, Symmetry groups in one dimension - Discrete symmetry groups, Symmetry groups in one dimension - Non-discrete symmetry groups, Symmetry groups in one dimension - Patterns without translational symmetry, Symmetry groups in one dimension - 1D-symmetry of a function vs. 2D-symmetry of its graph, Symmetry groups in one dimension - Group action, Symmetry groups in one dimension - Orbits and stabilizers

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(See (Voit 2003 § 5.4.3) and (Nolan 2005) The Lévy alpha-stable distributions have the "stability" property that if N alpha-stable variates Xi are drawn from the distribution then the sum will also be distributed as an alpha-stable variate, where T ...

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Levy skew alpha-stable distribution, Levy skew alpha-stable distribution - The distribution, Levy skew alpha-stable distribution - Special cases, Levy skew alpha-stable distribution - Stability property, Levy skew alpha-stable distribution - The generalized central limit theorem, Levy skew alpha-stable distribution - Series representation

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Matrix of the Free Trade Agreements in the region. 1 representing Kosovo as per Security Council resolution 1244. ██ instrument and year of entry into force ██ instrument and year of provisional entry into force See also:

Stability Pact for South Eastern Europe, Stability Pact for South Eastern Europe - Creation, Stability Pact for South Eastern Europe - Organization, Stability Pact for South Eastern Europe - Achievements, Stability Pact for South Eastern Europe - Regional Table, Stability Pact for South Eastern Europe - Working Table 1, Stability Pact for South Eastern Europe - Working Table 2, Stability Pact for South Eastern Europe - Working Table 3, Stability Pact for South Eastern Europe - FTA Progress, Stability Pact for South Eastern Europe - External link

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After some difficulties during the war (mainly because of the scarcity of paper towards the end of it, but also because American comics weren't allowed to be published anymore), Dupuis started to grow quickly. Le moustique became one of the leading magazines with info on radio and (later) television, and Spirou was one of the two leading European comic magazines (together with Tintin). Dupuis started publishing some books as well, but had real success by republishing the comics that had appeared as feuilletons in ...

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Dupuis, Dupuis - Overview, Dupuis - Origin, Dupuis - Growth after WWII, Dupuis - Stabilization and diversification

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  One major problem with both the diversity-productivity and diversity-stability debates discussed up to this point is that both focus on interactions at just a single trophic level. That is, they are concerned with only one level of the food web, namely plants. Other research, unconcerned with the effects of diversity, has demonstrated strong top-down forcing of ecosystems (see keystone species). There is very little actual data available regarding the effects of different food webs, but theory helps us in this area. Firs ...

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Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

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The element is of interest because it is part of the hypothesized island of stability, with isotope 304 being the most stable. ...

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Unbinilium, Unbinilium - History, Unbinilium - Stable Unbinilium

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  Ecological effects of biodiversity - How Species Diversity May Influence Productivity.   Complementarity – Plant species coexistence is thought to be the result of niche partitioning, or differences in resource requirements among species. By complementarity, a more diverse plant community should be able to use resources more completely, and thus be more productive (Fridley 2001, Tilman et al ...

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Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

Read more here: » Ecological effects of biodiversity: Encyclopedia II - Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY

  Ecological effects of biodiversity - Human Mediated Loss of Species.   It has become clear in recent years that we live on a human dominated earth. Ever growing human populations have caused ever increasing land and resource use. Human enterprises such as agriculture, industry, recreation, and international commerce have greatly affected land transformations, biotic additions and losses in the form of hunting, fishing, and invasions, and global biochemistry. These have in turn affected both clim ...

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Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

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The formal definition is as follows. Let a group G act on a topological space X by homeomorphisms. This action is called properly discontinuous if, for every x in X, there is a neighborhood U of x such that The set U is called a nice neighborhood of x. This narrow, basic definition fails when applied to a certain interesting case where one still wants to have a notion of discontinuity: the case where the stabilizer of the point x is non-tri ...

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Properly discontinuous, Properly discontinuous - Basic definition, Properly discontinuous - Definition with a non-trivial stabilizer, Properly discontinuous - Definition as a locally finite set

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As an example take a simple RC-filter. This continuous-time filter has a transfer function If we wish to implement this filter as a digital filter, we can apply the bilinear transform by substituting for s the formula above; after some reworking, we get the following filter representation: < ...

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Bilinear transform, Bilinear transform - Stability and minimum-phase property preserved, Bilinear transform - Example, Bilinear transform - Frequency warping

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Let f(z) be a polynomial (with complex coefficients) of degree n with no roots on the imaginary line (i.e. the line x=iy where i is the imaginary unit and x,y are real numbers). Let us define P0(y) (a polynomial of degree n) and P1(y) (a nonzero polynomial of degree strictly less than n) by f(iy) = P0(y) + iP1(y), respectively the real a ...

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Routh–Hurwitz theorem, Routh–Hurwitz theorem - Notations, Routh–Hurwitz theorem - Statement, Routh–Hurwitz theorem - Routh–Hurwitz stability criterion

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With the notations introduced above, the Routh–Hurwitz theorem states that: From the first equality we can for instance conclude that when the variation of the argument of f(iy) is positive, then f(z) will have more roots to the left of the imaginary axis than to its right. The equality p-q=w(+∞)-w(-∞) can be viewed as the complex counterpart of Sturm's theorem. Note the differences: in Sturm's theorem, the left member is p+q and th ...

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Routh–Hurwitz theorem, Routh–Hurwitz theorem - Notations, Routh–Hurwitz theorem - Statement, Routh–Hurwitz theorem - Routh–Hurwitz stability criterion

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AEGEE organises a wide range of projects, most of which relate to one of four main fields of action: Active Citizenship, Higher Education, Peace & Stability, and Cultural Exchange. AEGEE - Active Citizenship. AEGEE is an independent non-party political organisation, working closely with governments, institutions and other NGOs to realise its goals for Europe. AEGEE aims to provide a political voice for its members at every level, organising conferences on a range of topics and using the results to lobby European institutions. ...

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AEGEE, AEGEE - Description, AEGEE - History, AEGEE - Activities, AEGEE - Active Citizenship, AEGEE - Higher Education, AEGEE - Peace and Stability, AEGEE - Cultural Exchange

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Control systems exhibiting the Lur'e problem (after A.I.Lur'e) have a forward path that is linear and time-invariant, and a feedback path that contains a memory-less, and possibly time-varying, non-linearity. The linear part can be characterized by four matrices (A,B,C,D), while the non-linear part is Φ ∈ [a,b], a<b (a sector non-linearity). Non-linear control - Absolute stability problem. Consider: (A,B) is controllable and (C,A) is obser ...

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Non-linear control, Non-linear control - Properties of non-linear systems, Non-linear control - Analysis and control of non-linear systems, Non-linear control - The Lur'e problem, Non-linear control - Absolute stability problem

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If the optical cavity is not empty (e.g., a laser cavity which contains the gain medium), the value of L used is not the physical mirror separation but the optical path length between the mirrors. Lenses placed in the cavity alter the stability and mode size. In addition, for most gain media, thermal and other inhomogeneities create a lensing effect in the medium. Practical laser resonators may contain more than two mirrors; three- and four-mirror arrangements are common. This is called folding. These designs allow compensation ...

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Optical cavity, Optical cavity - Resonator modes, Optical cavity - Resonator types, Optical cavity - Stability, Optical cavity - Practical resonators, Optical cavity - Optical Delay Line

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When light from a star or another astronomical object enters the Earth's atmosphere, turbulence introduced (for example, by different temperature layers and different wind speeds interacting) distort and move the image in various ways (see astronomical seeing for a full discussion). Images produced by any telescope larger than a few centimeters are blurred by these distortions. For example, a 2.5 m telescope is reduced in resolution by a factor of between 7 and 20; in the case of very large telescopes (8-10 m) (like the VLT or Keck), which are theoretically capable of milli-arcsecond ...

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Adaptive optics, Adaptive optics - Introduction, Adaptive optics - Uses of adaptive optics, Adaptive optics - Beam stabilization

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People living in frequently shaken areas like Japan started early in developing earthquake resistant buildings based scientific study. Other countries likewise have and continue to study intensely how to make their citizens safer by understanding the problems posed by earthquakes more accurately. Until the last 75 years or so, the only way to run "frequent tests" was to build on a fault and hope. Even then, earthquakes may only happen at any given spot every couple of hundred years, and construction techniques may not therefore take a ...

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Earthquake construction, Earthquake construction - Development of Earthquake Construction Techniques, Earthquake construction - Modern Techniques, Earthquake construction - Ground stabilization

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Although widely used, MVC has both advantages and disadvantages compared to other design options, and individual circumstances should be used to choose the most appropriate design. Model-view-controller - View instability vs. model stability. If constructed correctly, models can enjoy a fair degree of stability (owing to the stability of the domain model), whereas user interface code usually undergoes frequent and sometimes dramatic change (typically because of usability problems, the need to support growi ...

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Model-view-controller, Model-view-controller - Operation, Model-view-controller - Advantages and disadvantages, Model-view-controller - View instability vs. model stability, Model-view-controller - Event driven, Model-view-controller - Implementations

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When we impose the constraints of causality and stability, the inverse system is unique; and the system and its inverse are called minimum-phase. The causality and stability constraints in the discrete-time case are the following: Minimum phase - Causality. Minimum phase - Stability. See the article on stability for ...

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Minimum phase, Minimum phase - Inverse system, Minimum phase - Discrete-time example, Minimum phase - Minimum phase system, Minimum phase - Causality, Minimum phase - Stability, Minimum phase - Frequency analysis, Minimum phase - Discrete-time frequency analysis, Minimum phase - Continuous-time frequency analysis, Minimum phase - Minimum phase in the time domain, Minimum phase - Minimum phase as minimum group delay, Minimum phase - Maximum phase, Minimum phase - Mixed phase

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The association was established in 1985, and now has about 15 000 members in 204 university cities in 40 countries throughout Europe. AEGEE promotes a unified Europe, cross-border co-operation, communication and integration in the academic environment. It is not linked to any political party, and has no national structures, operating only on the local and European levels. ...

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AEGEE, AEGEE - Description, AEGEE - History, AEGEE - Activities, AEGEE - Active Citizenship, AEGEE - Higher Education, AEGEE - Peace and Stability, AEGEE - Cultural Exchange

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