102,547 research outputs found
On Balancing of a Direct Product
No full textA direct product of two sequences is a naturally defined sequence on the
alphabet of pairs of symbols.
By taking inspiration from [Pavel Salimov. On uniform recurrence of a direct product. In AutoMathA, 2009], where the author investigates the case of uniformly recurrent words, here, we study when the product of two balanced sequences on binary alphabet is also balanced
Automated Stress Separation Along Stress Trajectories
No full textA procedure for the separation of principal stresses in automated photoelasticity is presented. It is based on the integration of indefinite equations of equilibrium along stress trajectories, also known as Lamè-Maxwell equations. A new algorithm for precise and reliable stress trajectory calculation, which is an essential feature of the procedure, has also been developed. Automated stress separation is carried out along stress trajectories starting from free boundaries. Experimental tests were performed on a disc in diametral compression and on a ring with internally applied pressure. Full-field principal stress values were obtained and results were compared with those from the theory of elasticity and with those obtained from the classical shear difference method. It was shown that the proposed method is more accurate and less affected by the presence of residual stresses or experimental errors at the boundaries than the shear difference method. In addition, the method requires little human interaction and is therefore well-suited for automated photoelasticity
Alkali-silica potentially reactive minerals in Lazio and Campania alluvial deposits (Italy).
No full textPrimitive sets of words
Get PDFGiven a (finite or infinite) subset X of the free monoid A⁎ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆F⁎. We say that a submonoid M generated by k elements of A⁎ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆A⁎ primitive if it is the basis of a |X|-maximal submonoid. This definition encompasses the notion of primitive word — in fact, {w} is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆Y⁎. We therefore call Y a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive root. To obtain this result, we prove that the intersection of two 2-maximal submonoids is either the empty word or a submonoid generated by one single primitive word. For a single word w, we say that the set {x,y} is a bi-root of w if w can be written as a concatenation of copies of x and y and {x,y} is a primitive set. We prove that every primitive word w has at most one bi-root {x,y} such that |x|+|y|<|w|. That is, the bi-root of a word is unique provided the word is sufficiently long with respect to the size (sum of lengths) of the root. Our results are also compared to previous approaches that investigate pseudo-repetitions, where a morphic involutive function θ is defined on A⁎. In this setting, the notions of θ-power, θ-primitive and θ-root are defined, and it is shown that any word has a unique θ-primitive root. This result can be obtained with our approach by showing that a word w is θ-primitive if and only if {w,θ(w)} is a primitive set
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