Simply connected object

Thus, for d > 4, the nature of the asymptotic behaviour is not modified on the contrary, for d < 4, summing divergencies may lead to the appearance of critical exponents. However, this argument is neither very simple nor very rigorous. It is, however, possible to reach the same conclusion in a much simpler and intuitive manner. In fact, let us consider, in a d-dimensional space domain, two simply connected objects with dimensions D and D respectively, and let us assume that they have a random position. If D + D < d, the probability that these objects have a common part has a zero measure. Actually, if they cut across each other, it is always possible to displace one object infinitesimally, so as to suppress the intersection. For instance, the statistics, of a set of segments (D = 1, D = 1) in a three-dimensional space (d = 3) is quite trivial, whereas in two dimensions, intersection effects have to be taken into account. Thus, in general, two objects feel exclusion effects if and only if D + D > d. 

Anomalous subdiffusion occurs on percolation clusters or on objects that in a statistical sense can be described as fractal, by which we mean that selfsimilarity describes simply the scaling of mass with length. Connections between v, the fractal dimension of the cluster, D, and the spectral dimension, d, have been established, relations that were originally derived by Alexander and Orbach [35], who developed a theory of vibrational excitations on fractal objects which they called fractons. An elegant scaling argument by Rammal and Toulouse [140] also leads to these relations, and we summarize their results. 

You can insert pictures, equations, and hyperlinks (to web sites), too. Choose Insert/ Picture and choose the picture you want. To enter an equation, Choose Insert/Object and choose Microsoft Equation. You may have to add that feature to your spreadsheet if it was not included during installation. (You need the original CD or ask your System Administrator to install it.) For hyperlinks, simply choose Insert/Hyperlinks and insert the web address. Be sure to try it while connected to the internet to ensure that it works. 

S represents a connector for electrical wires, which explains Itself. The part with a double loop may be attached to a fixed object by means of a screw. Another electrical connector is shown in T, one part of which consists of a spiral having an eye formed at each end for receiving the screws which fasten it to its support, the other part is simply a straight wire having an eye at one end. The connection is made by inserting the straight end in the spiral. To increase the friction of the two parts, either of them may be curved more or less. 

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