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A wide area measurement system (WAMS) is a technology developed to improve the stability of the power system in the past few decades, which provides a distributed control structure of a highly interconnected power system. However, the critical issues of security in WAMSs are rising to a new class of control problems due to the malicious attacks. This work studies the distributed model predictive control (DMPC) problem for wide area measurement power systems under malicious attacks. The malicious attacks model as time-varying data injection attacks which describe delayed input states. The traditional three-order model of an interconnection power system is modified to a distributed model with coupling control inputs. A sufficient condition to ensure that the closed loop system with asymptotic stability is obtained by using Lyapunov theorem and linear matrix inequality technology. An iterative DMPC algorithm is proposed to design the distributed controllers based on a cooperative control strategy. Finally, a simulation example of a three-machine nine-node power system is presented to verify the effectiveness of the proposed algorithm.

PurposeThe study attempted to gauge the relative effectiveness of celebrity and product image match-up in comparison to non-celebrity attractive endorsers for two distinct high involvement situations. Also, due to the expected demographic diversity among target consumers, the study aimed at assessing the impact of respondent's age and gender on the effectiveness of image match-up.Design/methodology/approachBuilding on the three-order hierarchy model, two experiments were conducted (utilising celebrity and non-celebrity endorsers) for two high involvement hierarchies, i.e. standard learning and dissonance/attribution. Through fictitious print advertisement, the experiments assessed the effectiveness of the match-up in terms of consumer attitudes towards advertisement and brand and intentions to purchase.FindingsThe match-up consistently and significantly outperformed non-celebrity attractive endorser in case of standard learning hierarchy. The same conclusion was not established for dissonance/attribution hierarchy due to the lack of significant results. The findings also suggest that the match-up subdues the impact of consumer's gender and age on consumer attitudes only in case of standard learning hierarchy.Research limitations/implicationsThe study provides interesting theoretical implication by challenging a widely held postulation about the applicability of celebrity and product match-up under high involvement.Practical implicationsThe research provides the practitioners with a better understanding of important issues, mainly, whether to use a celebrity endorser and selecting the right celebrity, especially if high involvement is expected.Originality/valuePrevious research concerning celebrity endorsements has largely considered consumer involvement as unitary, i.e. either high or low. However, the multifaceted aspect of consumer involvement is well established in the field of consumer psychology. The present research, therefore, is a pioneering attempt as it studies the effectiveness of match-up for two distinct high involvement situations. Moreover, unlike the majority of previous studies that have focused on the performance of “celebrity match” versus “celebrity mismatch”, the impact of match-up was studied in comparison to a non-celebrity attractive endorser.

Employing the inverse integral factor method, the first 13 quasi-Lyapunov constants for the three-order nilpotent critical point of a sextic Lyapunov system are deduced with the help of MATHEMATICS. Furthermore, sufficient and necessary center conditions are obtained, and there are 13 small amplitude limit cycles, which could be bifurcated from the three-order nilpotent critical point. Henceforth, we give a lower bound of limit cycles, which could be bifurcated from the three-order nilpotent critical point of sextic Lyapunov systems. At last, an example is given to show that there exists a sextic system, which has 13 limit cycles.

In this paper, we investigate the existence of positive solutions for singular third-order nonhomogeneous boundary value problems. By using a fixed point theorem of cone expansion-compression type due to Krasnosel’skii, we establish various results on the existence or nonexistence of single and multiple positive solutions to the singular boundary problems in the explicit intervals for the nonhomogeneous term. An example is also given to illustrate some of the main results.

In order to overcome the defects of the classical model in the description of the rheological properties of soft soil, an Abel glue pot was defined based on the fractional derivative theory by the fractional calculus of Riemann-Liouville. Three components fractional order derivative solid model was built with Abel glue pot. Then the experimental data was fit using the new model. The simulation results show that the three components fractional order derivative solid model is more accurately than the generalized Kelvin model or Burgers model and that it has few parameters.

This chapter contains sections titled: Key concepts Case: the rolling mill experiment Peek into the black box Background reading Summary

This chapter contains sections titled: C‐shaped cross‐section and bending–torsional loading Thin‐walled hollow cylinder Static and free‐vibration analyses of an airfoil‐shaped beam Free vibrations of a bridge‐like beam References

This book is an up-to-date introduction to simple theories and hyperimaginaries, with special attention to Lascar strong types and elimination of hyperimaginary problems. Assuming only knowledge of general model theory, the foundations of forking, stability and simplicity are presented in full detail. The treatment of the topics is as general as possible, working with stable formulas and types and assuming stability or simplicity of the theory only when necessary. The author offers an introduction to independence relations as well as a full account of canonical bases of types in stable and simple theories. In the last chapters the notions of internality and analyzability are discussed and used to provide a self-contained proof of elimination of hyperimaginaries in supersimple theories.

This book is a spectacular introduction to the modern mathematical discipline known as the Theory of Games. Harold Kuhn first presented these lectures at Princeton University in 1952. They succinctly convey the essence of the theory, in part through the prism of the most exciting developments at its frontiers half a century ago. Kuhn devotes considerable space to topics that, while not strictly the subject matter of game theory, are firmly bound to it. These are taken mainly from the geometry of convex sets and the theory of probability distributions. The book opens by addressing \"matrix games,\" a name first introduced in these lectures as an abbreviation for two-person, zero-sum games in normal form with a finite number of pure strategies. It continues with a treatment of games in extensive form, using a model introduced by the author in 1950 that quickly supplanted von Neumann and Morgenstern's cumbersome approach. A final section deals with games that have an infinite number of pure strategies for the two players. Throughout, the theory is generously illustrated with examples, and exercises test the reader's understanding. A historical note caps off each chapter. For readers familiar with the calculus and with elementary matrix theory or vector analysis, this book offers an indispensable store of vital insights on a subject whose importance has only grown with the years.