Gibbs phenomena for Lq-best approximation in finite element spaces

Recent developments in the context of minimum residual finite element methods are paving the way for designing quasi-optimal discretisation methods in non-standard function spaces, such as L q -type Sobolev spaces. For q → 1, these methods have demonstrated huge potential in avoiding the notorious Gibbs phenomena, i.e., the occurrence of spurious non-physical oscillations near thin layers and jump discontinuities. In this work we provide theoretical results that explain some of the numerical observations. In particular, we investigate the Gibbs phenomena for L q -best approximations of discontinuities in finite element spaces with 1 ≤ q < ∞. We prove sufficient conditions on meshes in one and two dimensions such that over- and undershoots vanish in the limit q → 1. Moreover, we include examples of meshes such that Gibbs phenomena remain present even for q = 1 and demonstrate that our results can be used to design meshes so as to eliminate the Gibbs phenomenon.

River water turbidity removal using new natural coagulant aids: case study of Euphrates River, Iraq

For turbidity removal, most of drinking water treatment plants are using coagulants due to the presence of suspended and colloidal materials at the coagulation and flocculation units. Aluminium and sulphates salts are the widely used coagulants, such as Aluminium sulphate (Alum) and ferric chloride. However, several researches have linked Alzheimer's disease to the use of Aluminium sulphate. Hence, scholars have conducted several researches on the possibility to reduce the amount of Aluminium sulphate by using natural material/plants base as coagulant aids. In this study, Mallow's Leaves Extracts (MLE) and Carob's Pods Extracts (CPE) were used as an alternative coagulant aid. Couples of coagulation tests were implemented to find the optimal dosage of Aluminium Sulphates were used as coagulants. The results displayed that the maximum turbidity removal efficiency by adding 100% of each coagulant (i.e., Alum, MLE and CPE) were (61.16%, 51.175% and 37.12%), respectively. In addition, the minimum residual turbidity and maximum turbidity removal efficiency were 4.56 NTU and 97.72% by adding 22.5 Alum and 7.5 MLE presenting 30 mg/l dosing. Further, the minimum residual turbidity and maximum turbidity removal efficiency were 15.4 NTU and 92.3% by adding 22.5 Alum and 7.5 CPE presenting 30 mg/l dosing.

How Does the Effect Fade over Distance? An Inquiry into the Decay Pattern of Distance Effect on Property Values in the Case of Taipei, Taiwan

It is generally accepted that the perception of homeowners towards certain potential risks or amenities fades as distance from the risk or amenity increases. This study aims to illustrate the distance–decay pattern with an appropriate mathematical function. Distance–decay functions and parameters that yield the minimum residual sum of squares (RSS) for a given regression model are considered to be the optimal approximation for the pattern of decay. The effect of flood risk and mass rapid transit (MRT) accessibility on residential housing prices in Taipei, Taiwan, are used as examples to test the optimization process. The results indicate that the type of distance function affects both the significance and the magnitude of the regression coefficients. In the case of Taipei, concave functions provide better fits for both the flood risk and MRT accessibility. RSS reduction is up to 10% compared to the blank. Surprisingly, the impact range for the flood risk is found to be larger than that for MRT accessibility, which suggested that the impact range of perception for uncertain risks is larger than expected.

DOA Estimation of LFM Signal Based on Krylov Subspace Method

Direction of arrival estimation (DOA) of LFM signal is an essential task in radar, sonar, acoustics and biomedical. In this paper, a short time Fourier transform multi-step knowledge aided iterative generalized minimum residual (STFT-MS-KAI-GMRES) approach is presented to amend the angle measurement of this signal. A three stage algorithm is proposed. First, the process is initiated with formulating an estimation algorithm for the carrier frequency and chirp rate, followed by calculation of STFT of the output of array element; this yields a spatial time-frequency distribution (STFD) matrix. Next, the Krylov subspace-based estimation algorithm is formulated in the presence of MS-KAI-ESPRIT algorithm. If the number of antennas increases, the accuracy of the algorithm will increase, but we will incur more communication costs. Results are presented showing attainment of the CRLB by STFT-MS-KAI-GMRES the for an adequately large signal to noise ratio (SNR). An important feature of the method presented in the current study is the low computational complexity that has higher suitability for practical applications.

NANOCELLULOSE FROM REED STALKS TO IMPROVE THE PROPERTIES OF PAPER FOR PACKAGING FOOD PRODUCTS

Background. The development of technologies for obtaining materials from plant raw materials, the use of which improves the consumer properties of cardboard and paper products and does not pollute the environment with harmful substances from synthetic polymers, is an urgent problem of our time. Objective. The purpose of the paper is to obtain pulp and nanocellulose from reed stalks by environmentally friendly methods and apply nanocellulose to improve the quality parameters of paper for packaging food products on automatic machines. Methods. To obtain pulp from reed stalks with a minimum residual content of lignin and minerals, two processing stages were used: alkaline extraction and organosolv cooking at a temperature of 97 ± 2 °C. Nanocellulose was obtained by the oxidation of organosolv reed pulp with 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) in the TEMPO / NaBr / NaClO system, which is more environmentally friendly than acid hydrolysis. The resulting nanocellulose was applied to paper samples from waste paper and sulphate unbleached pulp at a consumption from 1 to 3 g/m2. Results. Organosolv pulp was obtained from reed stalks with a residual lignin content of 0.53 % and an ash content of 0.045 %, which was used to obtain nanocellulose. The resulting nanocellulose particles have a transverse size in the range of 5–20 nm, a length of up to several micrometers, and the tensile strength of nanocellulose films is up to 60 MPa. It is shown that the application of nanocellulose to the surface of the samples increases the breaking strength and breaking length, and reduces the surface absorbency of paper. It was determined that with a nanocellulose consumption of up to 3 g/m2, paper samples have indicators that meet the requirements of the standard for paper for packaging food products on automatic machines. Conclusions. The use of nanocellulose from reed stalks as a hardening substance for paper production will allow replacing environmentally harmful polymer additives and up to 50 % of more expensive softwood pulp with waste paper, while maintaining paper quality indicators at the level of standard requirements.

Detection of CTNNB1 Hotspot Mutations in Cell-Free DNA from the Urine of Hepatocellular Carcinoma Patients

Hepatocellular carcinoma (HCC) is a leading cause of cancer-related deaths worldwide. The beta-catenin gene, CTNNB1, is among the most frequently mutated in HCC tissues. However, mutational analysis of HCC tumors is hampered by the difficulty of obtaining tissue samples using traditional biopsy. Here, we explored the feasibility of detecting tumor-derived CTNNB1 mutations in cell-free DNA (cfDNA) extracted from the urine of HCC patients. Using a short amplicon qPCR assay targeting HCC mutational hotspot CTNNB1 codons 32–37 (exon 3), we detected CTNNB1 mutations in 25% (18/73) of HCC tissues and 24% (15/62) of pre-operative HCC urine samples in two independent cohorts. Among the CTNNB1-mutation-positive patients with available matched pre- and post-operative urine (n = 13), nine showed apparent elimination (n = 7) or severalfold reduction (n = 2) of the mutation in urine following tumor resection. Four of the seven patients with no detectable mutations in postoperative urine remained recurrence-free within five years after surgery. In contrast, all six patients with mutation-positive in post-operative urine recurred, including the two with reduced mutation levels. This is the first report of association between the presence of CTNNB1 mutations in pre- and post-operative urine cfDNA and HCC recurrence with implications for minimum residual disease detection.

Ferrofluid Lubrication of Optimized Spiral-Grooved Conical Hybrid Journal Bearing using Current Carrying Wire Model

In order to systematically investigate the behaviour of fluid-film bearing, the determination of optimal parameters is of utmost importance. The core contributions of this paper are (1) modeling of the conical bearing for spiral-grooves with ferrofluid lubrication using current carrying wire model for fixed coordinate system, (2) deriving the expressions for magnetic field model and frictional power loss other than Reynolds equation for ferrofluid lubrication, and (3) evaluation of optimal values of spiral-grooved bearing surface for different cross-sectional shapes and that of current carrying wire model for magnetic field generation in ferrofluid lubrication. Generalized Minimum RESidual iterative solver and Newton-Raphson method has facilitated the solution of complex non-linear Finite Element (FE) formulated governing equations. Initially, the results have been obtained for determining the optimal values of spiral-groove and ferrofluid model attributes. After that, using these optimal values, corresponding performance indicators are evaluated. It was found that there exists a optimum value of different geometric features for distinct cross-sectional shapes of spiral-grooves.

Research on Optimizing Selection and Optimizing Matching Technologies of Aeroengine Fan Rotor Blades

Aiming at the problem of low resources utilization of rotating blades in the selection process of aeroengine fan rotor blades, this paper takes the first-order bending dispersion, first-order torque dispersion, and gravitational moment difference of rotor blades as the selection criteria and takes the minimum remaining blades as the optimization goal. An intelligent selection algorithm of blades based on the collocation degree of blades is proposed and achieves the efficient selection and full utilization of rotating blades. Aiming at the problem of multiple installations and multiple adjustments and low assembly success rate of fan rotor blades, this paper takes the gravity moment difference of the two blades at the diagonal position of 180° as the constraint and takes the minimum residual unbalance as the optimization objective, adopts the improved simulated annealing algorithm to optimize the assembly sequence of rotating blades, and greatly reduces the residual unbalance of blades, which is beneficial to reduce the number of assembly adjustments of blades. The optimizing selection and optimizing matching methods of rotating blades realize the full utilization and efficient assembly of blades and lays a foundation for the reliability and robustness of the assembly quality and service performance of blades.