Basic theorems of distributions and Fourier transforms

Master of ScienceDepartment of MathematicsMarianne KortenDistribution theory is an important tool in studying partial differential equations. Distributions are linear functionals that act on a space of smooth test functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. There are different possible choices for the space of test functions, leading to different spaces of distributions. In this report, we take a look at some basic theory of distributions and their Fourier transforms. And we also solve some typical exercises at the end

Anomalous orbital expansion of low-mass X-ray binary 2A 1822-371: the existence of a circumbinary disk?

The source 2A 1822-371 is an eclipsing low-mass X-ray binary (LMXB) consisting of a neutron star (NS) and a $\sim0.5~M_{\odot}$ donor star in an orbit of 5.57 hr. Based on timing of the eclipse arrival times, this source was found to be experiencing a rapid orbital expansion with an orbital-period derivative as $\dot{P}_{\rm orb}=(1.51\pm0.05)\times10^{-10}~\rm s\, s^{-1}$, implying that the mass-transfer rate should be higher than at least three times the Eddington accretion rate. The standard magnetic braking (MB) model cannot produce such a high mass-transfer rate. The modified MB model derived by Van \& Ivanova (2019) can produce a high mass-transfer rate, resulting in a high $\dot{P}_{\rm orb}$. This work proposes an alternative model to account for the anomalously high mass-transfer rate and $\dot{P}_{\rm orb}$ of 2A 1822-371. During the mass transfer, a tiny fraction of the transferred material is thought to form a circumbinary (CB) disk around the LMXB, which can efficiently extract orbital angular momentum from the system by the interaction between the CB disk and the binary. We use the MESA code to model the formation and evolution of 2A 1822-371 for different CB-disk masses. When the CB-disk mass is $2.3\times10^{-8}~ M_{\odot}$, the simulation can reproduce the observed donor-star mass, orbital period, and orbital-period derivative. Such a CB disk can accelerate the evolution of the binary and produce a high mass transfer rate of $1.9\times10^{-7}~ M_\odot\,\rm yr^{-1}$, driving the binary to evolve toward a wide-orbit system. Therefore, we propose that CB disks may be responsible for the rapid orbital changes observed in some LMXBs.Comment: 8 pages, 8 figures, Astronomy and Astrophysics in pres

Effective solid-to-fluid heat transfer coefficient in EGS reservoirs

The present work developed a three-equation local thermal non-equilibrium model to predict the effective solid-to-fluid heat transfer coefficient in the enhanced geothermal system reservoirs based on the volume averaging method. Due to the high rock-to-fracture size ratio, the solid thermal resistance effect in the internal rocks cannot be neglected in the effective solid-to-fluid heat transfer coefficient. The present three-equation local thermal non-equilibrium model can consider the dynamic variation of the solid thermal resistance in transient heat transfer by introducing the penetration temperature difference. The model was validated by comparison with pore-scale numerical simulations and macro-scale LTNE model numerical simulations. The results show that the three-equation local thermal non-equilibrium model has a high accurac

Force Sensorless Admittance Control for Teleoperation of Uncertain Robot Manipulator Using Neural Networks

In this paper, a force sensorless control scheme based on neural networks (NNs) is developed for interaction between robot manipulators and human arms in physical collision. In this scheme, the trajectory is generated by using geometry vector method with Kinect sensor. To comply with the external torque from the environment, this paper presents a sensorless admittance control approach in joint space based on an observer approach, which is used to estimate external torques applied by the operator. To deal with the tracking problem of the uncertain manipulator, an adaptive controller combined with the radial basis function NN (RBFNN) is designed. The RBFNN is used to compensate for uncertainties in the system. In order to achieve the prescribed tracking precision, an error transformation algorithm is integrated into the controller. The Lyapunov functions are used to analyze the stability of the control system. The experiments on the Baxter robot are carried out to demonstrate the effectiveness and correctness of the proposed control scheme

Healthcare workers' knowledge and attitudes regarding the World Health Organization's "my 5 moments for hand hygiene" : evidence from a Vietnamese central general hospital

Objectives: Although the World Health Organization (WHO) initiative "My 5 Moments for Hand Hygiene"has been lauded as effective in preventing hospital-associated infections, little is known about healthcare workers (HCWs)' hand hygiene behavior. In this study, we sought to assess knowledge and attitudes towards the concepts in this initiative, as well as associated factors, among Vietnamese HCWs at a general hospital. Methods: A structured questionnaire was administered to HCWs at a central Vietnamese general hospital in 2015. Multiple logistic regression analysis was used to identify factors associated with HCWs' knowledge and attitudes towards hand hygiene. Results: Of 120 respondents, 65.8% and 67.5% demonstrated appropriate knowledge and a positive attitude, respectively, regarding all 5 hand hygiene moments. Logistic regression indicated better knowledge of hand hygiene in workers who were over 30 years old, who were direct HCWs (rather than managers), who had frequent access to clinical information, and who received their clinical information from training. Those who worked in infectious and tropical disease wards, who had frequent access to clinical information, and who received information from training were more likely to have a positive attitude towards hand hygiene than their counterparts. Conclusions: Although many Vietnamese HCWs displayed moderate knowledge and positive attitudes towards the WHO hand hygiene guidelines, a key gap remained. Regular education and training programs are needed to increase knowledge and to improve attitudes and practices towards hand hygiene. Furthermore, a combination of multimodal strategies and locally-adapted interventions is needed for sustainable hand hygiene adherence. Copyright © 2020 The Korean Society for Preventive Medicine. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Huy Nguyen” is provided in this record*

Fraudulent User Detection Via Behavior Information Aggregation Network (BIAN) On Large-Scale Financial Social Network

Financial frauds cause billions of losses annually and yet it lacks efficient approaches in detecting frauds considering user profile and their behaviors simultaneously in social network . A social network forms a graph structure whilst Graph neural networks (GNN), a promising research domain in Deep Learning, can seamlessly process non-Euclidean graph data . In financial fraud detection, the modus operandi of criminals can be identified by analyzing user profile and their behaviors such as transaction, loaning etc. as well as their social connectivity. Currently, most GNNs are incapable of selecting important neighbors since the neighbors' edge attributes (i.e., behaviors) are ignored. In this paper, we propose a novel behavior information aggregation network (BIAN) to combine the user behaviors with other user features. Different from its close "relatives" such as Graph Attention Networks (GAT) and Graph Transformer Networks (GTN), it aggregates neighbors based on neighboring edge attribute distribution, namely, user behaviors in financial social network. The experimental results on a real-world large-scale financial social network dataset, DGraph, show that BIAN obtains the 10.2% gain in AUROC comparing with the State-Of-The-Art models.Comment: 6 pages, 1 figur

The Effectiveness of Tepid Sponge Bath with 32oc and 37oc to Decrease Body Temperature at Toddler with Fever

Introduction: Tepid sponge bath is a therapeutic bath by washing all around of the body with warm water to decrease body temperature. Warm water that used were 32oC (nail warm) and 37oC (warm). The aimed of this study was to compare the effectivity of tepid sponge bath with 32oC and 37oC warm water on decreasing body temperature at toddler with fever. Method: A quasy experimental pre post test design was used in this study. The population was toddler who had body temperature ≥38oC which treated in anggrek pediatric room dr. Iskak public hospital Tulungagung. There were 26 respondents recruited by using purposive sampling technique and divided into two group, each of 13 respondents received tepid sponge bath with 32oC and others received tepid sponge bath with 37oC warm water. The independent variable was tepid sponge bath and dependent variable was body temperature. Data were collected by using digital termometere and noted in respondent observation, then analyzed by using Paired t-Test and Mann Withney U-Test. Result: The result showed that there was an effectivity on decreasing body temperature by giving tepid sponge bath with 32oC and 37oC warm water with significance level p=0.000 and there was a difference decreasing body temperature among both of them with significance level p=0.016. Discussion: It can be concluded that tepid sponge bath with 37oC warm water was more effective than tepid sponge bath with 32oC warm water. Further studies should be observed the effectivity of tepid sponge bath with more specific age, fever character and more time and respondent

Frictional behaviour of non-crimp fabrics (NCFs) in contact with a forming tool

Microscopic observation and analysis are used to examine the role that contact conditions play in determining the frictional behaviour of non-crimp fabrics (NCFs). The true fibre contact length is measured over a range of normal pressures. For the NCF considered, the contact length is 67% lower than for a corresponding unidirectional tow-on-tool contact at a pressure of 240 kPa. The difference in contact behaviour is associated with the fabric architecture, specifically stitching and gaps between tows. These microscopic observations are used to predict friction using a constant interface shear strength model. These predictions are found to compare well with macroscopic friction measurements taken using a sliding sled arrangement, once the roughness of the sled tool is taken into account