In this paper, using probabilistic metric spaces techniques, we can weak the first moment condition for existence and uniqueness of selfsimilar fractal functions.

In a series of papers by D. Hughes, N. Hansen and their coauthors it was established that laminar microstructures developed in compression and rolling possess a surprising property: probability distribution of misorientations referred to the average misorientation is universal, i.e. slightly dependent on the material and the magnitude of plastic deformation. A similar fact was found for lamina ...

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-RossRubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit for...

This paper is devoted to explore tilted kinematic self-similar solutions of the the general cylindrical symmetric spacetimes. These solutions are of the first, zeroth, second and infinite kinds for the perfect fluid and dust cases. Three different equations of state are used to obtain these solutions. We obtain a total of five independent solutions. The correspondence of these solutions with th...

Comparisons over commutative expressions constitute a special problem in analogical mapping. The unique character of these comparisons stems from the nature of commutative expressions themselves, which encapsulate particular dimensions of similarity between their arguments. In this paper, we describe commutative matching mechanisms for two analogical mapping systems (SME and MAGI), and demonstr...

In this paper, we show that any scaled-up version of any discrete self-similar tree fractal does not strictly self-assemble, at any temperature, in Winfree’s abstract Tile Assembly Model.

In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of exist...

Abstract. We introduce a concept of similarity between vertices of directed graphs. Let GA and GB be two directed graphs with respectively nA and nB vertices. We define a nA × nB similarity matrix S whose real entry sij expresses how similar vertex i (in GA) is to vertex j (in GB) : we say that sij is their similarity score. In the special case where GA = GB = G, the score sij is the similarity...

A scalechart is a set of statecharts, operating in a dense time domain, whose behavior is self-similar at different scales. The simplicity of extracting proofs of behavior from scalecharts is demonstrated, based on the < and co relationships. An algorithm is presented which automatically extracts < relationships from a simplified version of scalecharts.

Network testing presents different challenges from software testing. One challenge is that only a small number of networks, at best, can actually be tested, even when the goal is to test a class of networks. One solution is to select a representative network, which will display any faults present in any network of the class. This paper introduces the use of “self-similarity” to select such a ne...