The maximum forcing number of polyomino

The forcing number of a perfect matching $M$ of a graph $G$ is the cardinality of the smallest subset of $M$ that is contained in no other perfect matchings of $G$. For a planar embedding of a 2-connected bipartite planar graph $G$ which has a perfect matching, the concept of Clar number of hexagonal system had been extended by Abeledo and Atkinson as follows: a spanning subgraph $C$ of is called a Clar cover of $G$ if each of its components is either an even face or an edge, the maximum number of even faces in Clar covers of $G$ is called Clar number of $G$, and the Clar cover with the maximum number of even faces is called the maximum Clar cover. It was proved that if $G$ is a hexagonal system with a perfect matching $M$ and $K'$ is a set of hexagons in a maximum Clar cover of $G$, then $G-K'$ has a unique 1-factor. Using this result, Xu {\it et. at.} proved that the maximum forcing number of the elementary hexagonal system are equal to their Clar numbers, and then the maximum forcing number of the elementary hexagonal system can be computed in polynomial time. In this paper, we show that an elementary polyomino has a unique perfect matching when removing the set of tetragons from its maximum Clar cover. Thus the maximum forcing number of elementary polyomino equals to its Clar number and can be computed in polynomial time. Also, we have extended our result to the non-elementary polyomino and hexagonal system

An all-digital charge to digital converter

PhD ThesisDuring the last two decades, the topic of the Internet of Things (IoT) has become very popular. It provides an idea that everything in the real world should be connected with the internet in the future. Integrating sensors into small wireless networked nodes is a huge challenge due to the low power/energy budget in wireless sensor systems. An integrated sensor normally consumes significant power and has complex design which increases the cost. The core part of the sensor is the sensor interface which consumes major power especially for a capacitor-based sensor. Capacitive sensors and voltage sensors are two frequently used sensor types in the wireless sensor family. Capacitive sensors, that transform capacitance values into digital outputs, can be used in areas such as biomedical, environmental, and mobile applications. Voltage sensors are also widely used in many modern areas such as Energy Harvesting (EH) systems. Both of these sensors may make use of sensor interfaces to transform a measured analogue signal into a frequency output or a digital code for use in a digital system. Existing sensor interfaces normally use complex analog-to-digital converter (ADC) techniques that consume high power and suffers from slow sensing response. This thesis proposes a smart all-digital dual-use capacitorbased sensor interface called charge to digital converter (QDC). This QDC is capable of not only sensing capacitance but also sensing voltages by using fully digital solutions based on iterative delay chain discharge. Unlike the conventional methods vii that only treats the sensed capacitance only as the input signal, this thesis proposes a method that can directly use the stored energy from the sensed capacitance as well to power parts of the circuit, which simplifies the design and saves power. By playing with the capacitance and input voltage, it can be used as a capacitance-to-digital converter (CDC) to sense capacitance under fixed input voltage and it also can be used as a capacitorbased voltage sensor interface to measure voltage level under fixed capacitance. The new method achieves the same accuracy with less than half the circuit size, and 25% and 33% savings on power and energy consumption compared with the state of art benchmark. The method has been validated by experimenting with a chip fabricated in 350nm process, in addition to extensive simulation analysis

How small things affect the big picture? The effect of service product innovation on perceived experience value

Purpose – By adopting retrospective evaluation theories, this study aims to explain how innovations provided by separate suppliers in the tourism value chain influence tourist’s perceived value of the overall experience, and further uncover which innovative product attributes are more effective in improving tourist perceptions of the overall value.Design/methodology/approach – A survey yielded 584 valid responses from tourists who had experienced specific tourist product innovations during their travels. Structural equation modelling was used to test the proposed theoretical model. Findings – The results reveal that tourists evaluate overall travelling experience value either by recalling an intense, impressive moment (i.e. a heuristic approach), or through an evaluation of the overall utility gained from the whole trip (i.e. a normative approach). Furthermore, innovations that are perceived as increasing convenience and enabling learning contribute to tourists’ overall value perception through both normative and heuristic approaches, while immersion resulting from innovation only contributes to overall perceived value through the heuristic approach.Practical implications – Given the complex service ecosystem of tourism destinations, each tourism service provider should consider how innovations contribute to the experience of the whole trip and which attributes of innovations increase tourists’ overall perceived experience value.Originality/value – This study complements existing knowledge by revealing the relationship between product innovation in tourism sectors and tourists’ perceived value of the whole trip. Moreover, it offers a theoretical framework for further investigation into service product innovation in hospitality and tourism industry

Convergence of Adam for Non-convex Objectives: Relaxed Hyperparameters and Non-ergodic Case

Adam is a commonly used stochastic optimization algorithm in machine learning. However, its convergence is still not fully understood, especially in the non-convex setting. This paper focuses on exploring hyperparameter settings for the convergence of vanilla Adam and tackling the challenges of non-ergodic convergence related to practical application. The primary contributions are summarized as follows: firstly, we introduce precise definitions of ergodic and non-ergodic convergence, which cover nearly all forms of convergence for stochastic optimization algorithms. Meanwhile, we emphasize the superiority of non-ergodic convergence over ergodic convergence. Secondly, we establish a weaker sufficient condition for the ergodic convergence guarantee of Adam, allowing a more relaxed choice of hyperparameters. On this basis, we achieve the almost sure ergodic convergence rate of Adam, which is arbitrarily close to $o(1/\sqrt{K})$. More importantly, we prove, for the first time, that the last iterate of Adam converges to a stationary point for non-convex objectives. Finally, we obtain the non-ergodic convergence rate of $O(1/K)$ for function values under the Polyak-Lojasiewicz (PL) condition. These findings build a solid theoretical foundation for Adam to solve non-convex stochastic optimization problems

Thermal, optical, interfacial and mechanical properties of titanium dioxide/shape memory polyurethane nanocomposites

To further understand effects of titanium dioxide (TiO2) nanoparticles on thermal, optical, microstructural, interfacial and mechanical properties of shape memory polyurethane (SMPU), TiO2/SMPU nanocomposites with different TiO2 contents were synthesized. Then various properties of TiO2/SMPU nanocomposites were characterized. Results indicate that the melting temperature of soft segments in SMPU can be used as the shape memory transition temperature of TiO2/SMPU nanocomposites. TiO2 nanoparticles are almost filled in SMPU pores to form compact skeleton structures in TiO2/SMPU when the TiO2 content is 3% by weight. Further, the used TiO2 is rutile phase, and lowers the SMPU crystallinity. The suitable TiO2 content can increase the absorptivity to UV light and enhance the reflectivity to visible light of TiO2/SMPU nanocomposites, lowering its photo-aging properties and prolonging its service life. Also, TiO2/SMPU shows a higher scattering intensity and a faster decreasing trend than SMPU due to the larger electron density difference between TiO2 and SMPU. The microphase separation and ordered structures in SMPU are decreased due to added TiO2 nanoparticles. There are electron density fluctuations at the interfaces between hard and soft phases in SMPU, and between SMPU and TiO2 nanoparticles. Finally, the prpared TiO2/SMPU nanocomposites have better shape memory effects and tensile properties when TiO2 content of 3% is proposed to synthesize TiO2/SMPU nanocomposites for practical engineering applications

Highly sensitive magnetic properties and large linear magnetoresistance in antiferromagnetic CrxSe(0.875\lex\le1)single crystals

CrxSe (x\le1) is a class of quasi-layered binary compounds with potential applications in spintronics due to its intriguing antiferromagnetic properties. In this work, CrxSe single crystals with high Cr content (x=0.87, 0.91 and 0.95) were grown, and their magnetic and transport properties were investigated in detail. It is found that with small increase of Cr content, the N\'eel temperature (TN) of the samples can dramatically increase from 147 K to 257 K, accompanied with obvious changes in the magnetic anisotropy and hysteresis. The phenomena of field-induced spin-flop transitions were unveiled in these alloys, indicating their comparatively low anisotropy. The magnetoresistance (MR) of the three compounds showed positive dependence at low temperatures and particularly, non-saturated linear positive MR was observed in Cr0.91Se and Cr0.95Se, with a large value of 16.2% achieved in Cr0.91Se (10K, 9T). The calculated Fermi surface and MR showed that the quasi-linear MR is a product of carrier compensation. Our work revealed highly sensitive magnetic and transport properties in the Cr-Se compounds, which can lay foundation when constructing further antiferromagnetic spintronic devices based on them

Simultaneous state and actuator fault estimation for satellite attitude control systems

AbstractIn this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The simulation results show satisfactory performance in estimating states and actuator faults. It also shows that multiple faults can be estimated successfully