Richardson Method Research Articles

On the Selection of Weights for Difference Schemes to Approximate Systems of Differential Equations

We consider the problem of determining the weights of difference schemes whose form is specified by a particular symbolic expression. The order of approximation of the differential equation is equal to a given number. To solve it, it was propose to proceed from considering systems of differential equations of a general form to one scalar equation. This method provides us with some values for the weights, which we propose to test using Richardson’s method. The method was shown to work in the case of low-order schemes. However, when transitioning from the scalar problem to the vector and nonlinear problems, the reduction of the order of the scheme, whose weights are selected for the scalar problem, occurs in different families of schemes. This was first discovered when studying the Shanks scheme, which belongs to the family of explicit Runge–Kutta schemes. This does not deteriorate the proposed strategy itself concerning the simplification of the weight-determination problem, which should include a clause on mandatory testing of the order using the Richardson method.

Semi-analytical solution of MHD free convective flow of a nanofluid over an exponentially stretching porous sheet in the presence of heat source/sink

In this study, the magnetohydrodynamic flow and heat transfer of electrically conducting nanofluid over an exponentially stretching porous sheet is investigated. By introducing similarity variables, the non-linear set of partial differential governing equations, are transformed into a system of ordinary nonlinear differential equations. The equations are solved semi-analytically by the Optimal Collocation Method (OCM) which is a powerful method to solve equations containing infinite boundary conditions. The accuracy of the OCM results is examined by the Richardson method. The effects of the different physical parameters such as magnetic field strength, nanofluid volume fraction, suction strength, and the heat sink/source value are discussed on the flow and heat transfer characteristics of the problem. The obtained results show that the velocity and temperature of nanofluid increase with the increase in volume fraction. Also, when suction increases, the thickness of the boundary layers decreases. As the strength of the magnetic field (Hartmann) increases, the temperature slightly increases but the flow rate of the nanofluid decreases. The skin friction coefficient and Nusselt number increase when the values of suction parameters, volume fraction, magnetic field, and the field angle increase.

Chip-scale all-optical complex-valued matrix inverter

Matrix inversion is a fundamental and widely utilized linear algebraic operation but computationally expensive in digital-clock-based platforms. Optical computing is a new computing paradigm with high speed and energy efficiency, and the computation can be realized through light propagation. However, there is a scarcity of experimentally implemented matrix inverters that exhibit both high integration density and the capability to perform complex-valued operations in existing optical systems. For the first time, we experimentally demonstrated an iterative all-optical chip-scale processor to perform the computation of complex-valued matrix inversion using the Richardson method. Our chip-scale processor achieves an iteration speed of 10 GHz, which can facilitate ultra-fast matrix inversion with the assistance of high-speed Mach–Zehnder interferometer modulators. The convergence can be attained within 20 iterations, yielding an accuracy of 90%. The proposed chip-scale all-optical complex-valued matrix inverter represents a distinctive innovation in the field of all-optical recursive systems, offering significant potential for solving computationally intensive mathematical problems.

On Implementation of Numerical Methods for Solving Ordinary Differential Equations in Computer Algebra Systems

This paper presents an original package for investigating numerical solutions of ordinary differential equations, which is built in the Sage computer algebra system. This project is focused on a closer integration of numerical and symbolic methods while primarily aiming to create a convenient tool for working with numerical solutions in Sage. The package defines two new classes: initial problems and approximate solutions. The first class defines tools for symbolic computations related to initial problems, while the second class defines tools for interpolating values of symbolic expressions on an approximate solution and estimating the error with the use of the Richardson method. An implementation of the Runge–Kutta method is briefly described, with its main feature being the possibility of working with arbitrary Butcher tableaux and arbitrary numeric fields.

Richardson Method for a Diffusion Equation with Functional Delay

Richardson Method for a Diffusion Equation with Functional Delay

A reevaluation of selected mortality risks in the updated NCI/NIOSH acrylonitrile cohort study.

The study aimed to determine whether the National Cancer Institute's (NCI) recent suggestion of associations between acrylonitrile (AN) exposure and mortality in lung and bladder cancer and pneumonitis is robust to alternative methods of data analysis. We used the Richardson method to indirectly adjust risk ratios (RRs) in relation to AN exposure for potential confounding by smoking and asbestos. We repeated key analyses omitting workers from Plant 4 to account for possible local, historical shipyard-related asbestos exposures. The adjustment of lung cancer RRs for confounding by both smoking and asbestos and omitting Plant 4 workers yielded mostly decreased RRs and much less evidence of a positive association with cumulative AN exposure. Overall, our reanalysis provided little evidence to support NCI's suggestion of associations between AN exposure and mortality in lung and bladder cancer and pneumonitis.

Richardson on moral innovation

Richardson on moral innovation

Influence of different temperatures on morphology and chemical state of the surface-active layer of scandium‑tungsten cathode

Scandium‑tungsten (ScW) cathodes have garnered a lot of research attention due to their high emission current density. Herein, the cathode working environment is simulated by heating in a vacuum chamber, and scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) are used to study the surface morphology and chemical oxidation states in the temperature range of 25 °C to 1300 °C. The results reveal that the surface of the tungsten matrix is obviously recrystallized with increasing temperature. Moreover, the scandium oxide becomes globular and clear depressions or holes occur in the aggregation region of the rare-earth oxide at the grain boundaries. The work function is measured by the Richardson method at room temperature, 1000 °C, and 1300 °C and is found to be 2.77, 2.72, and 2.88 eV, respectively. The work function of the cathode initially decreases with increasing temperature, followed by a gradual increase. This is due to the fact that active substances such as scandium oxide are severely lost at high temperatures, destroying the surface structure of the sample. As the Sc/W value decreases, the rate of depletion of active material from the surface is greater than the rate of replenishment of material to the surface.

Collective influences of boundary layer process and synoptic circulation on particulate pollution: A new study in changsha-zhuzhou-xiangtan urban agglomeration of central china

Particulate matter pollution is increasingly serious in Changsha-Zhuzhou-Xiangtan urban agglomeration (CZT) due to rapid industrialization and urbanization. Particulate matter pollution and weather conditions are closely related. In this study, the relationship between the large-scale weather circulation types (CTs), horizontal recirculation wind field, boundary layer structure and particulate matter pollution (PM2.5) in CZT was systematically investigated. Firstly, the Allwine and Whiteman (AW) wind field classification method and Richardson method were used to calculate the horizontal recirculation index and the planetary boundary layer height (PBLH) in CZT. By analyzing the relationship among the recirculation index, the PBLH and the particle concentration, it was found that the recirculation process in CZT could be divided into horizontal recirculation and “pseudo recirculation”. Then, the circulation patterns affecting the CZT were divided into nine types (CT1-CT9) by using T-mode PCA method based on 925 hpa geopotential data. The CZT was prone to recirculation under the control of high pressure rear (CT4), weak high pressure edge (CT5) and southwest vortex (CT7, CT8). It was found that CT4 and CT5 accompanied with lower PBLH and poorer vertical diffusion conditions characterized by high particle concentration. While CT7 and CT8 accompanied with higher PBLH and better vertical diffusion conditions characterized by low particle concentration. Finally, the effect of CTs, recirculation index and boundary layer structure on paticle matter concentration were assessed during two recirculation processes in December 2016 and August 2017, repectively. The analysis was complemented with FLEXPART-WRF model simulations, which confirmed that the recirculation and “pseudo recirculation” can be effectively distinguished by introducing the PBLH, combined with the large-scale weather circulation.

COMPARATIVE EVALUATION OF CYTOLOGICAL AND HISTOPATHOLOGICAL GRADING IN INVASIVE DUCTAL CARCINOMA BREAST: A CROSS-SECTIONAL STUDY

Objectives: Carcinoma breast is most commonly diagnosed cancer in women. Fine-needle aspiration cytology (FNAC) and histopathology play very important role in diagnosing breast cancer. Main objective of this study is to compare the cytological and histopathological grading in invasive ductal carcinoma of breast. Methods: The study was conducted in the Department of Pathology, Government Medical College, Patiala. Fifty patients with palpable breast lump were selected. The age of whom varied from 30 to 86 years. FNAC was done, smears were prepared and stained with Romanowsky and Papanicolaou stains. Cytological grading was done according to Robinson’s method. After surgery, the results were compared with histological grading according to Nottingham’s Modification of Bloom–Richardson method. Results: On cytological grading of 50 cases, 25 (50%) cases were graded as Grade II, 21 (42%) as Grade I, and 4 (8%) as Grade III. Whereas on histological grading, Grades I, II and III tumors were 17 (34%), 22 (44%), and 11 (22%), respectively. Overall concordance of cytological grading with histological grading was 76% with a kappa value of 0.605 and p<0.001. Conclusion: The study showed that the cytological grade correlates well with the histological grade. Cytological grade can be of great value in evaluating the aggressiveness of tumor, neoadjuvant chemotherapy and can be used as a prognostic factor for better management of patients.

Joint steepest descent and non‐stationary Richardson method for low‐complexity detection in massive MIMO systems

AbstractSignal detection is a major challenge in massive multiple‐input multiple‐output (MIMO) wireless systems due to array of hundreds of antennas. Linear minimum mean square error (MMSE) enables near‐optimal detection performance in massive MIMO but suffers from unbearable computational complexity due to complicated matrix inversions. To address this problem, we propose a novel low‐complexity signal detector based on joint steepest descent (SD) and non‐stationary Richardson (NSR) iteration method. The SD is applied to get an efficient searching direction for the following NSR method to enhance the performance. The key idea of the proposed algorithm is to utilize a combination of the scaled‐diagonal initialization and the system‐ and iteration‐dependent acceleration mechanism, so that the convergence can be significantly speeded up. An antenna‐ and eigenvalue‐based scaling parameter is introduced for the proposed detector to further improve the error‐rate performance. We also provide convergence guarantees for the proposed technique. Numerical results demonstrate that the proposed joint detection approach attains superior performance compared to existing iterative approaches and provides a lower computational complexity than the conventional MMSE detector.

A Positivity-Preserving Improved Nonstandard Finite Difference Method to Solve the Black-Scholes Equation

In this paper, we evaluate and discuss different numerical methods to solve the Black–Scholes equation, including the θ-method, the mixed method, the Richardson method, the Du Fort and Frankel method, and the MADE (modified alternating directional explicit) method. These methods produce numerical drawbacks such as spurious oscillations and negative values in the solution when the volatility is much smaller than the interest rate. The MADE method sacrifices accuracy to obtain stability for the numerical solution of the Black–Scholes equation. In the present work, we improve the MADE scheme by using non-standard finite difference discretization techniques in which we use a non-local approximation for the reaction term (we call it the MMADE method). We will discuss the sufficient conditions to be positive of the new scheme. Also, we show that the proposed method is free of spurious oscillations even in the presence of discontinuous initial conditions. To demonstrate how efficient the new scheme is, some numerical experiments are performed at the end.

Energy efficient data detection with low complexity for an uplink multi-user massive MIMO system

The current development of the Internet of Things (IoT) network in sixth-generation (6G) communication opens up various opportunities. When IoT devices with edge platforms connect to the telecommunication network, mobility, interferences, and intelligent device capacity issues might occur. The challenge with uplink MU-MIMO systems is data detection owing to noise, frequency allocations, and dense deployment of intelligent devices. The exponential complexity of extensive wireless networks makes optimal maximum likelihood detection impossible. Using MATLAB simulation-based analysis, we suggested an iterative data detection strategy based on a coordinate descent method (CDM) to reduce computing complexity while preserving an acceptable bit error rate (BER). Linear systems demand low co-channel interference (CCI) MU-MIMO uplink communications (CCI). A superior mean square error or BER performance is achieved using Maximum ratio combining with CDM. The proposed system outperforms the Richardson Method (RM), approximation message passing (AMP), and linear minimum mean square error (LMMSE) algorithms in terms of BER and complexity.

Understanding the Accuracy Limitations of Quantifying Methane Emissions Using Other Test Method 33A

Researchers have utilized Other Test Method (OTM) 33A to quantify methane emissions from natural gas infrastructure. Historically, errors have been reported based on a population of measurements compared to known controlled releases of methane. These errors have been reported as 2σ errors of ±70%. However, little research has been performed on the minimum attainable uncertainty of any one measurement. We present two methods of uncertainty estimation. The first was the measurement uncertainty of the state-of-the-art equipment, which was determined to be ±3.8% of the estimate. This was determined from bootstrapped measurements compared to controlled releases. The second approach of uncertainty estimation was a modified Hollinger and Richardson (H&R) method which was developed for quantifying the uncertainty of eddy covariance measurements. Using a modified version of this method applied to OTM 33A measurements, it was determined that uncertainty of any given measurement was ±17%. Combining measurement uncertainty with that of stochasticity produced a total minimum uncertainty of 17.4%. Due to the current nature of stationary single-sensor measurements and the stochasticity of atmospheric data, such uncertainties will always be present. This is critical in understanding the transport of methane emissions and indirect measurements obtained from the natural gas industry.

Low Complexity Linear Detectors for Massive MIMO with Several Antenna Array Configurations: A Comparative Study

In Multiple-Input Multiple-Output (MIMO), there is multi-user interference because of the limited number of antennas at the Base Station (BS). Deploying more antenna elements at the BS to decrease the multi-user interference is a costly solution. Therefore, changing the configuration of antenna arrays at the BS is implemented as an alternative. In this paper, the impact of BS antenna array configurations on the performance of massive MIMO detection techniques is investigated where four different antenna array configurations are implemented at the BS: Uniform Linear Array (ULA), Uniform Rectangular Planar Array (URPA), Uniform Circular Array (UCA) and Uniform Circular Planar Array (UCPA). The performance of the massive MIMO system is based on the millimeter wave (mmWave) channel that depends on the array response vector of the BS antenna array configuration. To the best of our knowledge, this is the first paper to investigate the impact of antenna array configurations at the BS on the performance and the computational complexity of massive MIMO detection techniques. Numerical results show that the implementation of URPA at the BS with MMSE detection algorithm can achieve the best performance of BER=10−4 at SNR = 9dB. The deployment of the UCA at the BS with the successive over-relaxation (SOR), the Gauss-Seidel (GS), and the conjugate-gradient (CG) detection methods provides a performance of BER=10−4 at SNR = 12dB when the number of iterations equals eight. In the case of using the UCA at BS with the Richardson (RI) detection method, the number of iterations is required to be increased to achieve the same performance. To achieve BER=10−4, the detector based on the CG method has the lowest computational complexity while the RI method has the highest complexity.

Computationally Efficient Data Detection in Massive MIMO Wireless Systems via Semi-Iterative Method

Practical data detectors must achieve low error-rate at low-complexity for massive multiple-input multiple-output (MIMO) wireless systems. Since near-optimal minimum mean square error (MMSE) detection exhibits high computational complexity for such wireless systems, various iterative methods as well as their enhanced variants have been proposed. The efficiency of iterative approaches, however, is not satisfying due to slow convergence rate and reduced accuracy. This paper proposes a novel semi-iterative data detection algorithm for massive MIMO systems that simultaneously achieves a large improvement in convergence and accuracy with respect to the corresponding iterative method. We provide a general three-term recurrence expression for semi-iterative detection and incorporate it with Richardson method as a show case. To further improve the convergence rate of the proposed technique, a new trace-diagonal based low-complexity initial method is developed. A sufficient condition for convergence of the proposed method is also provided. We analyze the associated complexity of semi-iterative detector, and provide numerical results which demonstrate that the proposed detector is superior to recently introduced iterative detectors in terms of both the error-rate performance and computational complexity.

SIMULATION OF A WATER CURTAIN APPLICATION TO PROTECT WORKERS FROM THERMAL INJURIES

Problem statement. The problem of evaluating the effectiveness of using the water curtain to reduce the risk of thermal injury to people in a fire is considered. The problem is to determine the temperature fields when supplying water for air cooling. The purpose of the article. Development of a numerical model for calculating the process of propagation of water droplets in the air, their evaporation to reduce the temperature of heated air due to fire. Methodology. For mathematical modeling of the process of propagation of water droplets in air, thermal air pollution, the convective-diffusion equation of mass transfer, the energy equation and the equation describing the motion of an ideal liquid (potential flow model) are used. The potential flow model allows you to quickly determine the field of air flow velocity in areas with a complex geometric shape. Implicit difference splitting schemes are used for numerical integration of the convective-diffusion mass transfer equation and the energy equation. Physical splitting of basic equations is used to construct a difference analogue of modeling equations. The Richardson method and the conditional approximation scheme are used to solve the aerodynamics problem of determining the velocity potential field and the components of the air velocity vector. An engineering method for calculating the process of evaporation of a drop of water based on Sreznevsky's law has been developed. Scientific novelty. An effective numerical model has been developed that allows the method of computational experiment to determine the efficiency of using the water curtain to reduce the level of thermal pollution of atmospheric air due to fire. The numerical model is based on the integration of the fundamental equations of aerodynamics, heat and mass transfer. The model takes into account the most significant physical factors that affect the process under study: the movement of heated air, the movement of water droplets in the air, evaporation of the droplet, and so on. Practical significance. Based on the built model, a computer code has been created that allows you to quickly determine the temperature fields in the air when using a water curtain. The numerical model will be useful when conducting computational experiments for the purpose of scientifically sound choice of the location of the water curtain in case of fire. Conclusions. A computer code has been created that allows a computational experiment to investigate the effectiveness of using a water curtain in a fire. The developed computer program can be implemented on low and medium power computers. The results of a computational experiment are presented.

Evaluation of homologous recombination deficiency (HRD) score and immuno-tumor microenvironment (iTME) as biomarkers of soft tissue sarcoma (STS) survival and response to immune checkpoint inhibitor therapy.

11568 Background: Soft tissue sarcoma (STS) are highly heterogenous in both histology and underlying genetic alterations, resulting in heterogenous outcomes of standard therapy. With recent stride of immunotherapies in oncology it is crucial to find the optimal match of the new therapies to disease subtypes. HRDScore and iTME parameters are two top candidate biomarkers to predict clinical outcomes in complex diseases such as STS. Methods: We prospectively profiled 102 Chinese STS patients who had received more than 1 line of prior treatment, mainly chemo-drugs. We then classified the patients according to their HRDScore (calculated from WES data using the Richardson method, ref. Telli M.L. et al. Clin. Cancer Res. 2016) and iTME parameters (calculated from RNAseq data using CIBERSORT method). Lastly, we tested the correlation of HRDScore or iTME with patient survival and clinic outcomes of anti-PD-1/L1 based combination therapy. Results: The histological subtypes of the patients included 32 LMS, 44 LPS, and 26 others (such as UPS, clear cell, myxofibrosarcoma, uterus LMS etc.). The top mutation genes (frequency > 5%) included TP53 29%, KMT2C 16%, NOTCH2 9%, ATRX 8%, NF1 8%, RB1 8% and PTEN 6%. The patients could be classified to HRD-high or HRD-low (HRDScore > or < = 42). Alternatively, unsupervised clustering of iTME revealed three patient subgroups (named iTME-I, -II, and -III). While all the three groups are characterized by a generally suppressed immune environment, iTME-I have high proportion of M0 macrophages and median M2 macrophages; iTME-II have high proportion of M2 macrophages but low M0 cells; and iTME-type III are low in both M0 and M2 cells. No significant M1 cells present in all the three iTME groups. Patient survivals were correlated with the iTME types but not HRDScore in Kaplan-Meyer analysis. The trend of survival time was iTME-III > iTME-II > iTME-I, with an HR = 0.156 for iTME-III over iTME-I (p = 0.008, log-rank test). Treatment response of anti-PD-1/L1 based combination therapies also showed a positive correlation to iTME-III, but not HRDScore although the small sample size prevented a definitive conclusion. Clinical evaluation of the 22 patients who received anti-PD-1/L1 therapy showed 1 PD (20%) and 4 SD/PR (80%) in iTME-III, 4 PD (40%) and 6 SD/PR (60%) in iTME-II, and 1 PD (33%) and 2 SD (67%) in iTME-I. Conclusions: iTME is a better biomarker than HRDScore in STS for survival and treatment outcomes. Differential Infiltration of M0 and M2 macrophages can distinguish patients with different survival and response to anti-PD-1/L1 combination therapy. The iTME subtypes may be used for treatment screen of combination immunotherapy but larger and randomized clinical studies are required to validate the discovery.

The Level of Knowledge of The Rural People on The Ecological And Biological Aspects of The Red Fox (vulpesvulpes) in Sharya Complex in Duhok Governorate in Kurdistan of Iraq Abstract:

The success of the development process requires the integration of its components of conscious human elements and material support, and given the importance of Rural people knowledge in all areas of knowledge, especially those related to the environmental and biological aspects of the red foxes (Vulpes vulpes), which are the focus of the current research due to their great impacts on the fields of farmers and rural people. This research aimed to identify the level of knowledge of the rural people about the ecological and biological information aspects of the red foxes in the (Sharya) complex, and the identification of the correlation between the level of the level of knowledge on the environmental and vital aspects of the red foxes as dependent variables and each of the following independent variables (age, gender, current occupation, educational level, and place of residence). A simple random sample of 126 was chosen representing 25% of the study population, with the exception of the pilot sample (30), via a special questionnaire form consisting of two parts, the first of which is related to the independent variables, the second includes a test consisting of 17 items distributed in two domains (environmental and biological).After ensuring their Face and content validity and validity of their contents, a consistency was measured by the Cuder Richardson method, followed by data collection and it was unpacked, categorized and statistically treated using a number of statistical methods. Due to the normal distribution of the data, Frequencies, Averages, Percentages, Spearman Correlation Coefficient, and Correlation Coefficient Pearson were used to analyze the data. This study revealed that, the level of knowledge of the rural people in the Sharya collective town is Medium in environmental and vital aspects with a percentage (61.9%) and (53.2%), respectively, and the study did not show a correlation between the level of Knowledge and the following factors: (age, place of residence, and current profession), while the study showed a correlation between the level of Knowledge and (educational level, and gender).

3D MODELING OF BIOLOGICAL WASTEWATER TREATMENT IN AERATION TANK

Purpose. The main purpose of the article is to develop a 3D CFD model for modeling the process of biological wastewater treatment in an aeration tank. Methodology. For mathematical modeling of the process of biological wastewater treatment in the reactor, taking into account the flow hydrodynamics, geometric shape of the aeration tank, convective-diffusion transfer of the substrate and activated sludge, a 3D CFD model was built. The model is based on the three-dimensional equation of motion of an ideal liquid and the equation of mass conservation for the substrate, activated sludge. The field of sewage flow rate in the aeration tank is calculated based on the velocity potential equation. The process of biological transformation of the substrate is calculated on the basis of the Monod model. The splitting scheme was used for numerical integration of the equations of convective-diffusion transfer of activated sludge and substrate. The splitting is carried out in such a way to take into account the transfer of substrate (activated sludge) in only one direction at each step of splitting. The calculation of the unknown value of the substrate (activated sludge) concentration is carried out according to an explicit scheme. The Richardson method is used to numerically integrate the three-dimensional equation for the velocity potential, and the unknown value of the velocity potential is calculated by an explicit formula. Euler's method is used for numerical integration of equations describing the process of substrate transformation and change in activated sludge concentration (Monod model). Findings. The software implementation of the constructed 3D CFD model is carried out. A description of the structure of the developed software package is provided. The results of a computer experiment to study the process of wastewater treatment in an aeration tank with additional elements are presented. Originality. A new multifactor 3D CFD model has been developed, which allows quick assessing the efficiency of biological treatment in an aeration tank. Practical value. The constructed 3D CFD model can be used to analyze the efficiency of the aeration tank under different operating conditions at the stage of sketch design of wastewater treatment systems.