The generalized Serre problem over <Emphasis Type="Italic">K</Emphasis>-Hermite rings

This paper investigates the completion and the zero prime factorization for matrices over a K-Hermite ring. The authors have generalized Kaplansky’s related results, solved similar Lin-Bose problem and generalized Serre problem over a K-Hermite ring.     

Performance comparison of distributed state estimation algorithms for power systems

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori (MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems.     

Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.     

Robust output regulation problem for discrete-time linear systems with both input and communication delays

Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discrete-time systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time timedelay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.     

Some open problems related to creative telescoping

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research. This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

Supply chain performance for deteriorating items with cooperative advertising

To study the effect of cooperative advertising on the supply chain of deteriorating items, this paper establishes a Stackelberg game model for a two-echelon deteriorating items supply chain composed of one manufacturer and one retailer under a given support program with an exogenous participation rate. The manufacturer as the leader determines the wholesale price and production rate, and the retailer as the follower determines the retail price and advertising strategies. The strategies of the players under the decentralized scenario and the centralized scenario are respectively characterized. Numerical simulations and sensitivity analysis are conducted to gain some managerial insights. It is shown that the pricing, advertising and production strategies are negatively correlated to deteriorating coefficient, and both the profit and the channel efficiency decrease with deteriorating coefficient; The interaction between price, advertising investment and production rate results in a higher retail price of the centralized channel compared to that of the decentralized channel; Implementing the cooperative advertising program does improve the performance of the supply chain in some cases and the participation rate roughly at 0.5 is most preferable, but it is also possible to distort incentive and damage the channel performance when the participation rate reaches a relatively high level.     

Advance selling in the presence of product diffusion effect

Product diffusion refers to the phenomenon that the later demand is dependent on the early sales. To investigate how a firm’s advance selling strategy is affected by the effect of product diffusion, we consider a monopolist seller who sells a fashionable product in a market that comprises of myopic and strategic consumers over two periods (i.e., the advance selling season and the regular selling season). For a linear product diffusion effect we find that, when the effect of product diffusion is positive, the seller may set an extremely high advance selling price to induce the strategic consumers to purchase in the regular selling season, which is counter-intuitive. Moreover, the optimal procurement quantity for the seller may increase in the negative effect of product diffusion and decrease in the amount of strategic consumers. When we extend our model to consider a concave quadratic product diffusion effect, however, the optimal procurement quantity is concave in the amount of strategic consumers. Numerical studies are further presented to discuss the managerial insights.     

Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.     

Risk reduction in a project portfolio

The positive impacts of managing projects as a portfolio are quantified by comparing the value of the integrated risk of a project portfolio and the aggregation of single project risks implemented separately. Firstly, the integrated risk is defined by proposing risky events based on set theory. Secondly, as projects interact with each other in a project portfolio, the integrated risk is evaluated by using a Bayesian network structure learning algorithm to construct an interdependent network of risks. Finally, the integrated risk of a practical case is assessed using this method, and the results show that the proposed method is an effective tool for calculating the extent of risk reduction of implementing a project portfolio and identifying the most risky project, so as to assist companies in making comprehensive decisions in the phase of portfolio selection and portfolio controlling.