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Injective parametrizations are widely used both in theory and in applications. The injectivity of parameteric curves and surfaces means that there are no self-intersections. Toric surface patch is defined by a set of integer lattice points A and corresponding control points and weights, which includes rational tensor product and triangle Bézier patches as special cases. In 2011, Sottile and Zhu presented a geometric method to check the injectivity of 2D toric surface patches. In this paper, we present an improved algorithm of their method. The complexity of the improved algorithm is reduced from O (n 3) to O (n 2) , where n = # (A). Some examples are shown to illustrate the effectiveness of our algorithm. Moreover, the algorithm is also applied to check the injectivity of parameterization in isogeometric analysis. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the properties of regular systems and improve the efficiency of the regular decomposition method RegSer implemented in Epsilon. We define a weaker concept which retains most properties of regular system. It can be shown that from a weak regular system one can also define a regular set and vice versa. We present an algorithm RecurWeakRegSer to decompose a given polynomial system into weak regular systems. When , the output of RecurWeakRegSer() often contains fewer components than that of RegSer(). This is one advantage of RecurWeakRegSer. Another one is that RecurWeakRegSer is more efficient than RegSer. This was shown by experiments that we carried out. Since it is an essential step in RegSer to compute subresultant polynomial remainder sequences (PRS), and there is some weakness in the implementation, we implement a new version of subresultant algorithm using the optimization strategy of Ducos so that the efficiency of RegSer can be improved. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the behavioral pseudometrics for probabilistic systems, which are a quantitative analogue of probabilistic bisimilarity in the sense that the distance zero captures the probabilistic bisimilarity. The model we are interested in is probabilistic automata, which are based on state transition systems and make a clear distinction between probabilistic and nondeterministic choices. The pseudometrics are defined as the greatest fixpoint of a monotonic functional on the complete lattice of state metrics. A distinguished characteristic of this pseudometric lies in that it does not discount the future, which addresses some algorithmic challenges to compute the distance of two states in the model. We solve this problem by providing an approximation algorithm: up to any desired degree of accuracy , the distance can be approximated to within in time exponential in the size of the model and logarithmic in . One of the key ingredients of our algorithm is to express a pseudometric being a post-fixpoint as the elementary sentence over real closed fields, which allows us to exploit Tarski’s decision procedure, together with the binary search to approximate the behavioral distance. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and study completely generalized multivalued nonlinear co-quasi-variational-like inclusions. By using J η-proximal mapping [1], we propose an iterative algorithm for computing the approximate solutions of completely generalized multivalued nonlinear co-quasi-variational-like inclusions problem. We prove that approximate solutions obtained by the proposed algorithm converge to the exact solutions of completely generalized multivalued nonlinear co-quasi-variational-like inclusions problem. Some special cases are also discussed. [Copyright &y& Elsevier]

Abstract: One of the main problems dealing with iterative methods for solving polynomial systemsis the initialization of the iteration. This paper provides an algorithm to initialize the search of solutions of polynomial systems. [Copyright &y& Elsevier]

Abstract: In this paper, we propose an algorithm for solving the obstacle problem. We try tofind the approximated region of the contact in the obstacle problem by iteration. Numerical examples are given for the obstacle problem for a membrane and the elastic-plastic torsion problem. [Copyright &y& Elsevier]

In this paper, we introduce a new algorithm for sign detection in a residue number system, which can be applied to any number of moduli set. This technique is faster than most competitive published works, based on MRC or CRT. The CRT requires large modulo M and is therefore costly to implement. The mix radix conversion (MRC) is a sequential process which causes long delay. The proposed algorithm is based on CRT 11. No big modulo M = Πi=1pin pi operations are needed for the CRT II. The modulo multipliers in the CRT II are bounded by size √M. The new sign detector uses less hardware than previous techniques. Using the new moduli set (2, 2n − 1, 2n + 2n−1 − 1, 2n+1 + 2n − 1), the implementation of a sign detector is further simplified. [Copyright &y& Elsevier]

A multiplier-free residue to binary converter architecture based on the Chinese remainder theorem II (CRT II) [1] is presented. The paper also includes a binary to residue converter. This is achieved by introducing a new moduli set (2, 2n − 1, 2n + 2n−1 − 1, 2n+1 + 2n − 1) for RNS application. The complexity of conversion has been greatly reduced using CRT II with the new moduli set. The proposed hardware architecture replaces the necessary multiplication by shift-left operations. A similar hardware architecture is presented for the binary to residue conversion. [Copyright &y& Elsevier]

In this paper, lower and upper bounds for min-max pair heap construction has been presented. It has been shown that the construction of a min-max pair heap with n elements requires at least 2.07n element comparisons. A new algorithm for creating min-max pair heap has been devised that lowers the upper bound to 2.43n. [Copyright &y& Elsevier]