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Abstract: A tree which has exactly one vertex of degree greater than two is said to be starlike. In spite of seemingly simple structure of these trees, not much is known about their spectral properties. In this paper, we introduce a generalization of the notion of cospectrality called -cospectrality which turns out to be useful in constructing cospectral graphs. Based on this, we construct cospectral mates for some starlike trees. We also present a set of necessary and sufficient conditions for divisibility of the characteristic polynomial of a starlike tree by the characteristic polynomial of a path. [Copyright &y& Elsevier]

Abstract: Measurement of short-term and long-term deflections is a necessary step towards understanding and evaluating the status of a bridge. In this paper, a novel non-contact weighted-stretched-wire (NCWSW) system is developed for measuring the deflection of a bridge. Also some factors related to the system are addressed. The proposed system is promising due to some attractive features such as high precision, low implementation cost and suitability for continuous monitoring. The efficiency and reliability of NCWSW system are investigated both analytically and experimentally. A realistic NCWSW system has been used in the monitoring of a real-world bridge. [Copyright &y& Elsevier]

Abstract: An RNA secondary structure is considered to be planar if its arc graph can be embedded into a plane without edge crossing. In this paper, a graphical criterion of planarity is presented based on graphical composition for RNA secondary structures with pseudoknots in Rivas–Eddy Class. Effective planar testing algorithms are introduced based on our graphical criterion. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to describe a simple dynamic crack propagation experiment which reproduces two phenomena: mixed-mode propagation and crack stop and restart. This experiment is explained and interpreted using X-FEM simulations. We show that a simple fracture theory which consists in using a dynamic crack initiation toughness, a crack orientation along the maximum principal stress and a simple equation for the calculation of the crack speed is sufficient to explain what is observed experimentally. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to show that various classes of operators having a common collection of root spaces whose closed linear span equals the entire space have dense sets of common cyclic vectors. [Copyright &y& Elsevier]

Abstract: This paper deals with a parabolic system, cross-coupled via a nonlinear source and a nonlinear boundary flux. We get a necessary and sufficient condition for the existence of non-simultaneous blow-up. In particular, four different simultaneous blow-up rates are obtained in different regions of parameters, described by an introduced characteristic algebraic system. It is observed that different initial data may result in different simultaneous blow-up rates even in the same region of parameters. [Copyright &y& Elsevier]

Abstract: Small pieces of metal are generated during trimming of automotive body panels. Commonly referred to as slivers, these pieces can be imprinted into the surface of stamped panels. This may require metalfinish of every stamped exterior panel. The objective of the paper is to study the influence of trimming conditions on quality of trimmed surface and to modify the trimming process to eliminate slivers and burrs from trimmed surface. This objective is being accomplished through numerical simulation of the blank fracture and experimental study of trimmed surface formation. Suggested solution includes two measures: (1) building an elastic support of the offal eliminating bending of the part of the blank being trimmed off; (2) creating the preference of crack propagation from the lower shearing edge by machining a small radius on the upper shearing edge. [Copyright &y& Elsevier]

Abstract: Given a set D of positive integers, the distance graph has vertices all integers Z, and two vertices j and in Z are adjacent if and only if . This paper determines the circular chromatic numbers of some distance graphs. [Copyright &y& Elsevier]