Boolean functions with optimal algebraic immunity (OAI functions) are important cryptographic primitives in the design of stream ciphers. During the past decade, a lot of work has been done on constructing such functions, among which mathematics, especially finite fields, play an important role. Notably, the approach based on decompositions of additive or multiplicative groups of finite fields turns out to be a very successful one in constructing OAI functions, where some original ideas are contributed by Tu and Deng (2012), Tang, et al. (2017), and Lou, et al. (2015). Motivated by their pioneering work, the authors and their collaborators have done a series of work, obtaining some more general constructions of OAI functions based on decompositions of finite fields. In this survey article, the authors review our work in this field in the past few years, illustrating the ideas for the step-by-step generalizations of previous constructions and recalling several new observations on a combinatorial conjecture on binary strings known as the Tu-Deng conjecture. In fact, the authors have obtained some variants or more general forms of Tu-Deng conjecture, and the optimal algebraic immunity of certain classes of functions we constructed is based on these conjectures.
相似文献The rational ruled surface is a typical modeling surface in computer aided geometric design. A rational ruled surface may have different representations with respective advantages and disadvantages. In this paper, the authors revisit the representations of ruled surfaces including the parametric form, algebraic form, homogenous form and Plücker form. Moreover, the transformations between these representations are proposed such as parametrization for an algebraic form, implicitization for a parametric form, proper reparametrization of an improper one and standardized reparametrization for a general parametrization. Based on these transformation algorithms, one can give a complete interchange graph for the different representations of a rational ruled surface. For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces, the characterization methods are recalled to identify the ruled surfaces from them.
相似文献This paper explores the risk factors threatening Zimbabwean Information Technology (IT) projects and build a systemic model demonstrating how the identified risk factors are interconnected. Drawn on systemic thinking, a soft systems approach called Interactive Management (IM) was adopted to identify the risk factors. The Interactive Management session involved the relevant stakeholders to interactively produce the systemic model through four major phases: idea generation, idea clarification, idea structuring, and interpretation of the structured ideas. The output of the Interactive Management process is a digraph showing the causal relationships between the identified risks. Six risk drivers were identified through the Interactive Management process: limited computer literacy, poor communication, lack of executive support, complexity of design, bureaucracy, and employee turnover. The constructed model demonstrates how the identified risk factors are interconnected. It also shows that non-linear relationships exist between risk factors. The output from this exploration has the potential to be used as a starting point to mitigate the risks impacting on Zimbabwean IT projects. Different from the output of frequently used approaches, the risk drivers identified in the systemic model inform decision makers to exploit the effective strategies in preventing other risks from materializing.
相似文献Safety is an essential requirement for control systems. Typically, controlled mobile robots are subject to safety constraints, to which control laws in typical forms may not be directly applicable. This paper employs barrier function to describe safety constraints, analyzes the interaction between the barrier function and the uncertain actuation dynamics by employing the ideas of interconnected systems, and proposes a quadratic-programming-based integration of the control algorithms subject to the safety constraint for a class of fully actuated systems.
相似文献In this paper, the authors study the multi-vehicle capacitated vehicle routing problem on a line-shaped network with unsplittable demand. The objective is to find a transportation scheme to minimize the longest distance traveled by a single vehicle such that all the customers are served without violating the capacity constraint. The authors show that this problem has no polynomial-time algorithm with performance ratio less than 2 on condition that P ≠ NP, and then provide a 2-approximation algorithm.
相似文献In this article, the problem of event-triggered adaptive fuzzy finite time control of non-strict feedback fractional order nonlinear systems is investigated. By using the property of fuzzy basis function, the obstacle caused by algebraic loop problems is successfully circumvented. Moreover, a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method, which can largely reduce the amount of communications. The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis. Finally, the effectiveness of the proposed scheme is verified by simulation examples.
相似文献This paper investigates the basis and pure Nash equilibrium of finite pure harmonic games (FPHGs) based on the vector space structure. First, a new criterion is proposed for the construction of pure harmonic subspace, based on which, a more concise basis is constructed for the pure harmonic subspace. Second, based on the new basis of FPHGs and auxiliary harmonic vector, a more easily verifiable criterion is presented for the existence of pure Nash equilibrium in basis FPHGs. Third, by constructing a pure Nash equilibrium cubic matrix, the verification of pure Nash equilibrium in three-player FPHGs is given.
相似文献The performances of preliminary test estimators for error variance based on W, LR and LM tests in a normal linear model are considered in this paper. Firstly, the risks of the proposed estimators are derived and compared by theoretical analysis and numerical calculation, respectively. The results show that their risks are related to the equality constraint error and the critical value of test. Moreover, the minimum value of the risks can be achieved when the critical value of test equals to one. Secondly, the superiority conditions of the proposed estimators are discussed. Finally, the results are illustrated by a simulation example.
相似文献