Foliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology*Entropy* **2016**, *18*(12), 433; doi:10.3390/e18120433 (registering DOI) - 2 December 2016**Abstract **
IN MEMORIAM OF ALEXANDER GROTHENDIECK. THE MAN.
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EEG-Based Person Authentication Using a Fuzzy Entropy-Related Approach with Two Electrodes*Entropy* **2016**, *18*(12), 432; doi:10.3390/e18120432 (registering DOI) - 2 December 2016**Abstract **

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Person authentication, based on electroencephalography (EEG) signals, is one of the directions possible in the study of EEG signals. In this paper, a method for the selection of EEG electrodes and features in a discriminative manner is proposed. Given that EEG signals are

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Person authentication, based on electroencephalography (EEG) signals, is one of the directions possible in the study of EEG signals. In this paper, a method for the selection of EEG electrodes and features in a discriminative manner is proposed. Given that EEG signals are unstable and non-linear, a non-linear analysis method, i.e., fuzzy entropy, is more appropriate. In this paper, unlike other methods using different signal sources and patterns, such as rest state and motor imagery, a novel paradigm using the stimuli of self-photos and non-self-photos is introduced. Ten subjects are selected to take part in this experiment, and fuzzy entropy is used as a feature to select the minimum number of electrodes that identifies individuals. The experimental results show that the proposed method can make use of two electrodes (FP1 and FP2) in the frontal area, while the classification accuracy is greater than 87.3%. The proposed biometric system, based on EEG signals, can provide each subject with a unique key and is capable of human recognition.
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Maximum Entropy Production Is Not a Steady State Attractor for 2D Fluid Convection*Entropy* **2016**, *18*(12), 431; doi:10.3390/e18120431 (registering DOI) - 1 December 2016**Abstract **

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Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends

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Multiple authors have claimed that the natural convection of a fluid is a process that exhibits maximum entropy production (MEP). However, almost all such investigations were limited to fixed temperature boundary conditions (BCs). It was found that under those conditions, the system tends to maximize its heat flux, and hence it was concluded that the MEP state is a dynamical attractor. However, since entropy production varies with heat flux and difference of inverse temperature, it is essential that any complete investigation of entropy production allows for variations in heat flux and temperature difference. Only then can we legitimately assess whether the MEP state is the most attractive. Our previous work made use of negative feedback BCs to explore this possibility. We found that the steady state of the system was far from the MEP state. For any system, entropy production can only be maximized subject to a finite set of physical and material constraints. In the case of our previous work, it was possible that the adopted set of fluid parameters were constraining the system in such a way that it was entirely prevented from reaching the MEP state. Hence, in the present work, we used a different set of boundary parameters, such that the steady states of the system were in the local vicinity of the MEP state. If MEP was indeed an attractor, relaxing those constraints of our previous work should have caused a discrete perturbation to the surface of steady state heat flux values near the value corresponding to MEP. We found no such perturbation, and hence no discernible attraction to the MEP state. Furthermore, systems with fixed flux BCs actually minimize their entropy production (relative to the alternative stable state, that of pure diffusive heat transport). This leads us to conclude that the principle of MEP is not an accurate indicator of which stable steady state a convective system will adopt. However, for all BCs considered, the quotient of heat flux and temperature difference $F/\Delta T$ —which is proportional to the dimensionless Nusselt number—does appear to be maximized.
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Fiber-Mixing Codes between Shifts of Finite Type and Factors of Gibbs Measures*Entropy* **2016**, *18*(12), 428; doi:10.3390/e18120428 - 30 November 2016**Abstract **

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A sliding block code $\pi :X\to Y$ between shift spaces is called fiber-mixing if, for every *x* and ${x}^{\prime}$ in *X* with $y=\pi \left(x\right)=\pi \left({x}^{\prime}\right)$ , there is $z\in {\pi}^{}$

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A sliding block code $\pi :X\to Y$ between shift spaces is called fiber-mixing if, for every *x* and ${x}^{\prime}$ in *X* with $y=\pi \left(x\right)=\pi \left({x}^{\prime}\right)$ , there is $z\in {\pi}^{-1}\left(y\right)$ which is left asymptotic to *x* and right asymptotic to ${x}^{\prime}$ . A fiber-mixing factor code from a shift of finite type is a code of class degree 1 for which each point of *Y* has exactly one transition class. Given an infinite-to-one factor code between mixing shifts of finite type (of unequal entropies), we show that there is also a fiber-mixing factor code between them. This result may be regarded as an infinite-to-one (unequal entropies) analogue of Ashley’s Replacement Theorem, which states that the existence of an equal entropy factor code between mixing shifts of finite type guarantees the existence of a degree 1 factor code between them. Properties of fiber-mixing codes and applications to factors of Gibbs measures are presented.
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CoFea: A Novel Approach to Spam Review Identification Based on Entropy and Co-Training*Entropy* **2016**, *18*(12), 429; doi:10.3390/e18120429 - 30 November 2016**Abstract **

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With the rapid development of electronic commerce, spam reviews are rapidly growing on the Internet to manipulate online customers’ opinions on goods being sold. This paper proposes a novel approach, called CoFea (Co-training by Features), to identify spam reviews, based on entropy and

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With the rapid development of electronic commerce, spam reviews are rapidly growing on the Internet to manipulate online customers’ opinions on goods being sold. This paper proposes a novel approach, called CoFea (Co-training by Features), to identify spam reviews, based on entropy and the co-training algorithm. After sorting all lexical terms of reviews by entropy, we produce two views on the reviews by dividing the lexical terms into two subsets. One subset contains odd-numbered terms and the other contains even-numbered terms. Using SVM (support vector machine) as the base classifier, we further propose two strategies, CoFea-T and CoFea-S, embedded with the CoFea approach. The CoFea-T strategy uses all terms in the subsets for spam review identification by SVM. The CoFea-S strategy uses a predefined number of terms with small entropy for spam review identification by SVM. The experiment results show that the CoFea-T strategy produces better accuracy than the CoFea-S strategy, while the CoFea-S strategy saves more computing time than the CoFea-T strategy with acceptable accuracy in spam review identification.
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On Macrostates in Complex Multi-Scale Systems*Entropy* **2016**, *18*(12), 426; doi:10.3390/e18120426 (registering DOI) - 29 November 2016**Abstract **

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A characteristic feature of complex systems is their deep structure, meaning that the definition of their states and observables depends on the level, or the scale, at which the system is considered. This scale dependence is reflected in the distinction of micro- and

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A characteristic feature of complex systems is their deep structure, meaning that the definition of their states and observables depends on the level, or the scale, at which the system is considered. This scale dependence is reflected in the distinction of micro- and macro-states, referring to lower and higher levels of description. There are several conceptual and formal frameworks to address the relation between them. Here, we focus on an approach in which macrostates are contextually emergent from (rather than fully reducible to) microstates and can be constructed by contextual partitions of the space of microstates. We discuss criteria for the stability of such partitions, in particular under the microstate dynamics, and outline some examples. Finally, we address the question of how macrostates arising from stable partitions can be identified as relevant or meaningful.
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Healthcare Teams Neurodynamically Reorganize When Resolving Uncertainty*Entropy* **2016**, *18*(12), 427; doi:10.3390/e18120427 (registering DOI) - 29 November 2016**Abstract **

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Research on the microscale neural dynamics of social interactions has yet to be translated into improvements in the assembly, training and evaluation of teams. This is partially due to the scale of neural involvements in team activities, spanning the millisecond oscillations in individual

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Research on the microscale neural dynamics of social interactions has yet to be translated into improvements in the assembly, training and evaluation of teams. This is partially due to the scale of neural involvements in team activities, spanning the millisecond oscillations in individual brains to the minutes/hours performance behaviors of the team. We have used intermediate neurodynamic representations to show that healthcare teams enter persistent (50–100 s) neurodynamic states when they encounter and resolve uncertainty while managing simulated patients. Each of the second symbols was developed situating the electroencephalogram (EEG) power of each team member in the contexts of those of other team members and the task. These representations were acquired from EEG headsets with 19 recording electrodes for each of the 1–40 Hz frequencies. Estimates of the information in each symbol stream were calculated from a 60 s moving window of Shannon entropy that was updated each second, providing a quantitative neurodynamic history of the team’s performance. Neurodynamic organizations fluctuated with the task demands with increased organization (i.e., lower entropy) occurring when the team needed to resolve uncertainty. These results show that intermediate neurodynamic representations can provide a quantitative bridge between the micro and macro scales of teamwork.
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Measurement on the Complexity Entropy of Dynamic Game Models for Innovative Enterprises under Two Kinds of Government Subsidies*Entropy* **2016**, *18*(12), 424; doi:10.3390/e18120424 (registering DOI) - 29 November 2016**Abstract **

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In this paper, setting the high-tech industry as the background, we build a dynamic duopoly game model in two cases with different government subsidies based on the innovation inputs and outputs, respectively. We analyze the equilibrium solution and stability conditions of the system,

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In this paper, setting the high-tech industry as the background, we build a dynamic duopoly game model in two cases with different government subsidies based on the innovation inputs and outputs, respectively. We analyze the equilibrium solution and stability conditions of the system, and study the dynamic evolution of the system under the conditions of different system parameters by the numerical simulation method. The simulation results show that both innovation subsidy policies have positive effects on firms’ innovation activities. Besides, improving the level of innovation can encourage firms to innovate. It also shows that an exaggerated adjusting speed of innovation outputs may cause complicated dynamic phenomena such as bifurcation and chaos, which means that the system has relatively higher entropy than that in a stable state. The degree of the government innovation subsidies is also shown to impact the stability and entropy of the system.
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Anisotropically Weighted and Nonholonomically Constrained Evolutions on Manifolds*Entropy* **2016**, *18*(12), 425; doi:10.3390/e18120425 - 26 November 2016**Abstract **

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We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and are anisotropic distributed. The family can be

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We present evolution equations for a family of paths that results from anisotropically weighting curve energies in non-linear statistics of manifold valued data. This situation arises when performing inference on data that have non-trivial covariance and are anisotropic distributed. The family can be interpreted as most probable paths for a driving semi-martingale that through stochastic development is mapped to the manifold. We discuss how the paths are projections of geodesics for a sub-Riemannian metric on the frame bundle of the manifold, and how the curvature of the underlying connection appears in the sub-Riemannian Hamilton–Jacobi equations. Evolution equations for both metric and cometric formulations of the sub-Riemannian metric are derived. We furthermore show how rank-deficient metrics can be mixed with an underlying Riemannian metric, and we relate the paths to geodesics and polynomials in Riemannian geometry. Examples from the family of paths are visualized on embedded surfaces, and we explore computational representations on finite dimensional landmark manifolds with geometry induced from right-invariant metrics on diffeomorphism groups.
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Condensation: Passenger Not Driver in Atmospheric Thermodynamics*Entropy* **2016**, *18*(12), 417; doi:10.3390/e18120417 - 25 November 2016**Abstract **

The second law of thermodynamics states that processes yielding work or at least capable of yielding work are thermodynamically spontaneous, and that those costing work are thermodynamically nonspontaneous. Whether a process yields or costs heat is irrelevant. Condensation of water vapor yields work

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The second law of thermodynamics states that processes yielding work or at least capable of yielding work are thermodynamically spontaneous, and that those costing work are thermodynamically nonspontaneous. Whether a process yields or costs heat is irrelevant. Condensation of water vapor yields work and hence is thermodynamically spontaneous only in a supersaturated atmosphere; in an unsaturated atmosphere it costs work and hence is thermodynamically nonspontaneous. Far more of Earth’s atmosphere is unsaturated than supersaturated; based on this alone evaporation is far more often work-yielding and hence thermodynamically spontaneous than condensation in Earth’s atmosphere—despite condensation always yielding heat and evaporation always costing heat. Furthermore, establishment of the unstable or at best metastable condition of supersaturation, and its maintenance in the face of condensation that would wipe it out, is always work-costing and hence thermodynamically nonspontaneous in Earth’s atmosphere or anywhere else. The work required to enable supersaturation is most usually provided at the expense of temperature differences that enable cooling to below the dew point. In the case of most interest to us, convective weather systems and storms, it is provided at the expense of vertical temperature gradients exceeding the moist adiabatic. Thus, ultimately, condensation is a work-costing and hence thermodynamically nonspontaneous process even in supersaturated regions of Earth’s or any other atmosphere. While heat engines in general can in principle extract all of the work represented by any temperature difference until it is totally neutralized to isothermality, convective weather systems and storms in particular cannot. They can extract only the work represented by partial neutralization of super-moist-adiabatic lapse rates to moist-adiabaticity. Super-moist-adiabatic lapse rates are required to enable convection of saturated air. Condensation cannot occur fast enough to maintain relative humidity in a cloud exactly at saturation, thereby trapping some water vapor in metastable supersaturation. Only then can the water vapor condense. Thus ultimately condensation is a thermodynamically *non*spontaneous process *forced* by super-moist-adiabatic lapse rates. Yet water vapor plays vital roles in atmospheric thermodynamics and kinetics. Convective weather systems and storms in a dry atmosphere (e.g., dust devils) can extract only the work represented by partial neutralization of super-dry-adiabatic lapse rates to dry-adiabaticity. At typical atmospheric temperatures in the tropics, where convective weather systems and storms are most frequent and active, the moist-adiabatic lapse rate is much smaller (thus much closer to isothermality), and hence represents much more extractable work, than the dry—the thermodynamic advantage of water vapor. Moreover, the large heat of condensation (and to a lesser extent fusion) of water facilitates much faster heat transfer from Earth’s surface to the tropopause than is possible in a dry atmosphere, thereby facilitating much faster extraction of work, i.e., much greater power, than is possible in a dry atmosphere—the kinetic advantage of water vapor.
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Consensus of Second Order Multi-Agent Systems with Exogenous Disturbance Generated by Unknown Exosystems*Entropy* **2016**, *18*(12), 423; doi:10.3390/e18120423 - 25 November 2016**Abstract **

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This paper is concerned with consensus problem of a class of second-order multi-agent systems subjecting to external disturbance generated from some unknown exosystems. In comparison with the case where the disturbance is generated from some known exosystems, we need to combine adaptive control

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This paper is concerned with consensus problem of a class of second-order multi-agent systems subjecting to external disturbance generated from some unknown exosystems. In comparison with the case where the disturbance is generated from some known exosystems, we need to combine adaptive control and internal model design to deal with the external disturbance generated from the unknown exosystems. With the help of the internal model, an adaptive protocol is proposed for the consensus problem of the multi-agent systems. Finally, one numerical example is provided to demonstrate the effectiveness of the control design.
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Energy Efficiency Improvement in a Modified Ethanol Process from Acetic Acid*Entropy* **2016**, *18*(12), 422; doi:10.3390/e18120422 - 24 November 2016**Abstract **

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For the high utilization of abundant lignocellulose, which is difficult to directly convert into ethanol, an energy-efficient ethanol production process using acetic acid was examined, and its energy saving performance, economics, and thermodynamic efficiency were compared with the conventional process. The raw ethanol

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For the high utilization of abundant lignocellulose, which is difficult to directly convert into ethanol, an energy-efficient ethanol production process using acetic acid was examined, and its energy saving performance, economics, and thermodynamic efficiency were compared with the conventional process. The raw ethanol synthesized from acetic acid and hydrogen was fed to the proposed ethanol concentration process. The proposed process utilized an extended divided wall column (DWC), for which the performance was investigated with the HYSYS simulation. The performance improvement of the proposed process includes a 27% saving in heating duty and a 41% reduction in cooling duty. The economics shows a 16% saving in investment cost and a 24% decrease in utility cost over the conventional ethanol concentration process. The exergy analysis shows a 9.6% improvement in thermodynamic efficiency for the proposed process.
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The Information Geometry of Sparse Goodness-of-Fit Testing*Entropy* **2016**, *18*(12), 421; doi:10.3390/e18120421 - 24 November 2016**Abstract **

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This paper takes an information-geometric approach to the challenging issue of goodness-of-fit testing in the high dimensional, low sample size context where—potentially—boundary effects dominate. The main contributions of this paper are threefold: first, we present and prove two new theorems on the behaviour

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This paper takes an information-geometric approach to the challenging issue of goodness-of-fit testing in the high dimensional, low sample size context where—potentially—boundary effects dominate. The main contributions of this paper are threefold: first, we present and prove two new theorems on the behaviour of commonly used test statistics in this context; second, we investigate—in the novel environment of the extended multinomial model—the links between information geometry-based divergences and standard goodness-of-fit statistics, allowing us to formalise relationships which have been missing in the literature; finally, we use simulation studies to validate and illustrate our theoretical results and to explore currently open research questions about the way that discretisation effects can dominate sampling distributions near the boundary. Novelly accommodating these discretisation effects contrasts sharply with the essentially continuous approach of skewness and other corrections flowing from standard higher-order asymptotic analysis.
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Prediction of Bearing Fault Using Fractional Brownian Motion and Minimum Entropy Deconvolution*Entropy* **2016**, *18*(11), 418; doi:10.3390/e18110418 - 23 November 2016**Abstract **

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In this paper, we propose a novel framework for the diagnosis of incipient bearing faults and trend prediction of weak faults which result in gradual aggravation with the bearing vibration intensity as the characteristic parameter. For the weak fault diagnosis, the proposed framework

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In this paper, we propose a novel framework for the diagnosis of incipient bearing faults and trend prediction of weak faults which result in gradual aggravation with the bearing vibration intensity as the characteristic parameter. For the weak fault diagnosis, the proposed framework adopts the improved minimum entropy deconvolution (MED) theory to identify the weak fault characteristics of mechanical equipment. From a large number of actual data analysis, once a bearing shows a weak fault, the bearing vibration intensity not only has random non-stationary, but also long-range dependent (LRD) characteristics. Therefore, the stochastic model with LRD−fractional Brown motion (FBM) is proposed to evaluate and predict the condition of slowly varying bearing faults which is a gradual process from weak fault occurrence to severity. For the FBM stochastic model, we mainly implement the derivation and the parameter identification of the FBM model. This is the first study to slowly fault prediction with stochastic model FBM. Experimental results show that the proposed methods can obtain the best performance in incipient fault diagnosis and bearing condition trend prediction.
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Simple Harmonic Oscillator Canonical Ensemble Model for Tunneling Radiation of Black Hole*Entropy* **2016**, *18*(11), 415; doi:10.3390/e18110415 - 23 November 2016**Abstract **

A simple harmonic oscillator canonical ensemble model for Schwarzchild black hole quantum tunneling radiation is proposed in this paper. Firstly, the equivalence between canonical ensemble model and Parikh–Wilczek’s tunneling method is introduced. Then, radiated massless particles are considered as a collection of simple

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A simple harmonic oscillator canonical ensemble model for Schwarzchild black hole quantum tunneling radiation is proposed in this paper. Firstly, the equivalence between canonical ensemble model and Parikh–Wilczek’s tunneling method is introduced. Then, radiated massless particles are considered as a collection of simple harmonic oscillators. Based on this model, we treat the black hole as a heat bath to derive the energy flux of the radiation. Finally, we apply the result to estimate the lifespan of a black hole.
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Periodic Energy Transport and Entropy Production in Quantum Electronics*Entropy* **2016**, *18*(11), 419; doi:10.3390/e18110419 - 23 November 2016**Abstract **

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The problem of time-dependent particle transport in quantum conductors is nowadays a well established topic. In contrast, the way in which energy and heat flow in mesoscopic systems subjected to dynamical drivings is a relatively new subject that cross-fertilize both fundamental developments of

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The problem of time-dependent particle transport in quantum conductors is nowadays a well established topic. In contrast, the way in which energy and heat flow in mesoscopic systems subjected to dynamical drivings is a relatively new subject that cross-fertilize both fundamental developments of quantum thermodynamics and practical applications in nanoelectronics and quantum information. In this short review, we discuss from a thermodynamical perspective recent investigations on nonstationary heat and work generated in quantum systems, emphasizing open questions and unsolved issues.
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On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations*Entropy* **2016**, *18*(11), 420; doi:10.3390/e18110420 - 23 November 2016**Abstract **

In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some

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In this manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.
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Analysis of the Complexity Entropy and Chaos Control of the Bullwhip Effect Considering Price of Evolutionary Game between Two Retailers*Entropy* **2016**, *18*(11), 416; doi:10.3390/e18110416 - 19 November 2016**Abstract **

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In this research, a model is established to represent a supply chain, which consists of one manufacturer and two retailers. The price-sensitive demand model is considered and the price game system is built according to the rule of bounded rationality as well as

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In this research, a model is established to represent a supply chain, which consists of one manufacturer and two retailers. The price-sensitive demand model is considered and the price game system is built according to the rule of bounded rationality as well as the entropy theory. With the increase of the price adjustment speed, the game system may go into chaos from the stable and periodic state. The bullwhip effect and inventory variance ratio of different stages that the system falls in are compared in real time. We also employ the delayed feedback control method to control the system and succeed in mitigating the bullwhip effect of the system. On the whole, the bullwhip effect and inventory variance ratio in the stable state are smaller than those in period-doubling and chaos. In the stable state, there is an optimal price adjustment speed to obtain both the lowest bullwhip effect and inventory variance ratio.
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Application of Sample Entropy Based LMD-TFPF De-Noising Algorithm for the Gear Transmission System*Entropy* **2016**, *18*(11), 414; doi:10.3390/e18110414 - 18 November 2016**Abstract **

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This paper investigates an improved noise reduction method and its application on gearbox vibration signal de-noising. A hybrid de-noising algorithm based on local mean decomposition (LMD), sample entropy (SE), and time-frequency peak filtering (TFPF) is proposed. TFPF is a classical filter method in

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This paper investigates an improved noise reduction method and its application on gearbox vibration signal de-noising. A hybrid de-noising algorithm based on local mean decomposition (LMD), sample entropy (SE), and time-frequency peak filtering (TFPF) is proposed. TFPF is a classical filter method in the time-frequency domain. However, there is a contradiction in TFPF, i.e., a good preservation for signal amplitude, but poor random noise reduction results might be obtained by selecting a short window length, whereas a serious attenuation for signal amplitude, but effective random noise reduction might be obtained by selecting a long window length. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, LMD and SE are adopted to improve TFPF. Firstly, the original signal is decomposed into PFs by LMD, and the SE value of each product function (PF) is calculated in order to classify the numerous PFs into the useful component, mixed component, and the noise component; then short-window TFPF is employed for the useful component, long-window TFPF is employed for the mixed component, and the noise component is removed; finally, the final signal is obtained after reconstruction. The gearbox vibration signals are employed to verify the proposed algorithm, and the comparison results show that the proposed SE-LMD-TFPF has the best de-noising results compared to traditional wavelet and TFPF method.
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Existence of Solutions to a Nonlinear Parabolic Equation of Fourth-Order in Variable Exponent Spaces*Entropy* **2016**, *18*(11), 413; doi:10.3390/e18110413 - 18 November 2016**Abstract **

This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent ${v}_{t}+{\mathrm{div}(|\nabla \u25b5v|}^{p(x)-2}{}^{}$

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This paper is devoted to studying the existence and uniqueness of weak solutions for an initial boundary problem of a nonlinear fourth-order parabolic equation with variable exponent ${v}_{t}+{\mathrm{div}(|\nabla \u25b5v|}^{p(x)-2}{\nabla \u25b5v)-|\u25b5v|}^{q(x)-2}\u25b5v=g(x,v)$ . By applying Leray-Schauder’s fixed point theorem, the existence of weak solutions of the elliptic problem is given. Furthermore, the semi-discrete method yields the existence of weak solutions of the corresponding parabolic problem by constructing two approximate solutions.
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