Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states

Investigation on the static fatigue mechanism and effect of specimen thickness on the static fatigue lifetime in WC–Co cemented carbides

The static fatigue mechanism and effect of specimen thickness on static fatigue lifetime for four WC–Co cemented carbides were studied with different binder contents and carbide grain sizes. Static fatigue tests under three-point bend loading were conducted on different sized specimens. The fracture surfaces of rupture specimens were examined by scanning electron microscopy to investigate the static fatigue micromechanisms.Досліджено механізм статичної втоми і вплив товщини зразка на термін служби при статичній втомі для чотирьох твердих сплавів WC–Co з різним вмістом зв’язки і розміром зерен. Випробування на статичну втому при навантаженні за схемою триточкового вигину було проведено на зразках різних розмірів. Поверхні зламів зруйнованих зразків було вивчено c допомогою скануючої електронної мікроскопії з метою дослідження мікромеханізму статичної втоми.Исследованы механизм статической усталости и влияние толщины образца на срок службы при статической усталости для четырех твердых сплавов WC–Co с различным содержанием связующего и размером зерен. Испытания на статическую усталость при нагрузке по схеме трехточечного изгиба были проведены на образцах различных размеров. Поверхности изломов разрушенных образцов были изучены c помощью сканирующей электронной микроскопии с целью исследования микромеханизмов статической усталости

Robust control of uncertain nonlinear systems: a nonlinear DOBC approach

This paper advocates disturbance observer based control (DOBC) for uncertain nonlinear systems. Within this framework, a nonlinear controller is designed based on the nominal model in the absence of disturbance and uncertainty where the main design specifications are to stabilize the system and achieve good tracking performance. Then a nonlinear disturbance observer is designed to not only estimate external disturbance but also system uncertainty/ unmodelled dynamics. With described uncertainty, rigorous stability analysis of the closed-loop system under the composite controller is established in this paper. Finally, the robust control problems of a missile roll stabilization and a mass spring system are addressed to illustrative the distinct features of the nonlinear DOBC approach

Law Article-Enhanced Legal Case Matching: a Causal Learning Approach

Legal case matching, which automatically constructs a model to estimate the similarities between the source and target cases, has played an essential role in intelligent legal systems. Semantic text matching models have been applied to the task where the source and target legal cases are considered as long-form text documents. These general-purpose matching models make the predictions solely based on the texts in the legal cases, overlooking the essential role of the law articles in legal case matching. In the real world, the matching results (e.g., relevance labels) are dramatically affected by the law articles because the contents and the judgments of a legal case are radically formed on the basis of law. From the causal sense, a matching decision is affected by the mediation effect from the cited law articles by the legal cases, and the direct effect of the key circumstances (e.g., detailed fact descriptions) in the legal cases. In light of the observation, this paper proposes a model-agnostic causal learning framework called Law-Match, under which the legal case matching models are learned by respecting the corresponding law articles. Given a pair of legal cases and the related law articles, Law-Match considers the embeddings of the law articles as instrumental variables (IVs), and the embeddings of legal cases as treatments. Using IV regression, the treatments can be decomposed into law-related and law-unrelated parts, respectively reflecting the mediation and direct effects. These two parts are then combined with different weights to collectively support the final matching prediction. We show that the framework is model-agnostic, and a number of legal case matching models can be applied as the underlying models. Comprehensive experiments show that Law-Match can outperform state-of-the-art baselines on three public datasets.Comment: 10 pages accepted by SIGIR202

Robust wavefront dislocations of Friedel oscillations in gapped graphene

Friedel oscillation is a well-known wave phenomenon, which represents the oscillatory response of electron waves to imperfection. By utilizing the pseudospin-momentum locking in gapless graphene, two recent experiments demonstrate the measurement of the topological Berry phase by corresponding to the unique number of wavefront dislocations in Friedel oscillations. Here, we study the Friedel oscillations in gapped graphene, in which the pseudospin-momentum locking is broken. Unusually, the wavefront dislocations do occur as that in gapless graphene, which expects the immediate verification in the current experimental condition. The number of wavefront dislocations is ascribed to the invariant pseudospin winding number in gaped and gapless graphene. This study deepens the understanding of correspondence between topological quantity and wavefront dislocations in Friedel oscillations, and implies the possibility to observe the wavefront dislocations of Friedel oscillations in intrinsic gapped two-dimensional materials, e.g., transition metal dichalcogenides.Comment: 5 pages, 3 figure