The cyclic shift graph of a monoid is the graph whose vertices are the elements of the monoid and whose edges connect elements that are cyclic shift related. The Patience Sorting algorithm admits two generalizations to words, from which two kinds of monoids arise, the $\belr$ monoid and the $\bell$ (also known as Bell) monoid. Like other monoids arising from combinatorial objects such as the plactic and the sylvester, the connected components of the cyclic shift graph of the $\belr$ monoid consists of elements that have the same number of each of its composing symbols. In this paper, with the aid of the computational tool SageMath, we study the diameter of the connected components from the cyclic shift graph of the $\belr$ monoid.

Within the theory of monoids, the cyclic shift relation, among other relations, generalizes the relation of conjugacy for groups. We examine several of these relations for both the $\belr$ and the $\bell$ monoids.

Abstract This paper addresses the durability of bond between concrete and carbon fibre reinforced polymer (CFRP) strips installed according to the near-surface mounted (NSM) technique (NSM CFRP-concrete systems) under the effects of two main groups of environmental conditions: (i) laboratory-based ageing conditions; (ii) real outdoor ageing conditions. The bond degradation was evaluated by carrying out direct pullout tests on aged specimens that were previously subjected to distinct environmental conditions for different periods of exposure. Moreover, the degradation of the mechanical properties of the involved materials was investigated. The digital image correlation (DIC) method was used to document the evolution of the deformation fields at the surface over the whole region of interest consisting of concrete and epoxy adhesive at the ligament region. This information supported the discussion about the evolution of the bond resistant mechanism developed in \{NSM\} CFRP-concrete specimens during testing, as well as the assessment of the bond quality of the system. In general, the results obtained from the durability tests conducted have shown that the different exposure environments, which may be considered as quite severe, did not result in significant damage on \{NSM\} CFRP-concrete system. The maximum decrease of about 12% on bond strength was obtained for real outdoor environments. Conversely, a maximum increase of 8% on bond strength was obtained on the specimens exposed to the temperature cycles between -15��C and +60��C. \{DIC\} allowed to document the stress transfer mechanisms established between the \{CFRP\} and the concrete substrate, revealing the crack patterns and the influence widths of the \{CFRP\} reinforcement strips, which were shown to be important for avoiding group effect when using multiple parallel strengthening \{CFRP\} strips.

The paper presents a nonlinear analytical solution for the prediction of the full-range debonding response of mechanically-anchored FRP composites from the substrate. The nonlinear analytical approach predicts, for any monotonic loading history or bonded length the relative displacements (or slips) between materials, the strains in the FRP composite, the bond stresses within the interface and the stresses developed in the substrate. The load-slip responses FRP-to-substrate interfaces with a short and a long bonded lengths are motive of analysis and discussion. The solutions obtained from the proposed approach are also compared with other experimental results found in the literature.

http://docentes.fct.unl.pt/lblm/files/bba-2018-1866-373.pdf

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Tourism is an industry that has been growing rapidly in the last few years and it is expected that it will continue to grow. Due to the evolution of technology, mobile applications are being increasingly used in all kinds of industries, being one of them tourism. Presently there are already a few mobile applications used to increase the experience of the user when visiting a place, but these mobile applications lack some important features. This paper describes the development of a mobile application with integrated routing algorithms used to increase the experience of the tourists when visiting the city of Avila, Spain. The tourist will have at their disposal real time information about all the monuments available for visit, a full set of predefined circuits with different visit times and degrees of difficulty and also the possibility to create an optimized or personalized circuit combining the user preferences such as visiting time and number of monuments to visit.