Ball Method Research Articles

An Adaptive Heavy Ball Method for Ill-Posed Inverse Problems

An Adaptive Heavy Ball Method for Ill-Posed Inverse Problems

Higher-Order Iterative Learning Control Algorithms for Linear Systems

Iterative learning control (ILC) algorithms appeared in connection with the problems of increasing the accuracy of performing repetitive operations by robots. They use information from previous repetitions to adjust the control signal on the current repetition. Most often, information from the previous repetition only is used. ILC algorithms that use information from several previous iterations are called higher-order algorithms. Recently, interest in these algorithms has increased in the literature in connection with robotic additive manufacturing problems. However, in addition to the fact that these algorithms have been little studied, there are conflicting estimates regarding their properties. This paper proposes new higher-order ILC algorithms for linear discrete and differential systems. The idea of these algorithms is based on an analogy with multi-step methods in optimization theory, in particular, with the heavy ball method. An example is given that confirms the possibility to accelerate convergence of the learning error when using such algorithms.

Greedy Randomized Kaczmarz with momentum method for nonlinear equation

Based on the nonlinear greedy randomized Kaczmarz (NGRK) method and the heavy ball method, a nonlinear greedy randomized Kaczmarz with momentum (NGRKm) method is presented for solving large nonlinear systems. Furthermore, the convergence of the NGRKm method is proved and the corresponding numerical experiments show the effectiveness of the NGRKm method.

The effect of cardiac rehabilitation prescription on medication complications and ET-1, WMSI in elderly patients with coronary heart disease

ObjectiveTo explore the effects of cardiac rehabilitation prescriptions on medication complications, Endothelin 1 (ET-1), and Wall Motion Score Index (WMSI) in elderly patients with coronary heart disease.Methods98 elderly patients with coronary heart disease admitted to the Department of Cardiology of a hospital from January 2020 to June 2022 are selected. According to the red and blue ball method, 98 research subjects are divided into a control group and an observation group. The control group receives routine treatment and exercise intervention, while the observation group receives cardiac rehabilitation prescriptions. After a follow-up of 6 months, the incidence of medication complications between the two groups is compared. The changes in ET-1 and WMSI levels are compared before treatment, 1 month, 3 months, and 6 months after treatment.ResultsThe two groups had no significant difference in ET-1 and WMSI levels before intervention. After intervention, both groups showed significant reductions in ET-1 and WMSI compared with baseline. The ET-1 of the observation group decreased significantly faster than the control group after 1 month, 3 months, and 6 months of intervention. The WMSI decreased more significantly at 6 months. The repeated measurement variance showed that there was a significant difference in the trend of ET-1 changes between the two groups, while the difference between the WMSI groups was not significant. The incidence of medication complications in the observation group was 10.20%, significantly lower than the 26.53% in the control group.ConclusionCardiac rehabilitation prescriptions can reduce the incidence of medication complications in elderly patients with coronary heart disease. It can reduce ET-1 levels faster, improve myocardial motor function, which has better myocardial function and medication safety than conventional treatment.

Research and application of migration and plugging mechanism of temporary plugging balls in multicluster fracturing of horizontal wells

Plugging and diverting stimulation technology using temporary plugging balls (PDSTB) in horizontal wells is one of the effective measures to enhance production in heterogeneous carbonate reservoirs. However, the migration and plugging mechanism of temporary plugging balls in horizontal wells remain unclear, leading to suboptimal field application. Based on the Lagrangian method, the migration and plugging models of temporary plugging balls were established. The study investigated the migration and plugging mechanism of temporary plugging balls. It analyzed the effects of parameters such as displacement on the plugging efficiency. The results show that the flow field in the perforation section is significantly affected by the displacement. Temporary plugging balls show three states of plugging: one ball plugging one shot-hole, multiple balls plugging one shot-hole, and balls remaining in the wellbore. The plugging efficiency initially increases, and then, decreases with the increase in displacement and the ball diameter. The plugging efficiency initially increases, and then, stabilizes with the increase in the viscosity of the carrying fluid and the usage ratio of balls. Plugging efficiency decreases with increasing density of balls. The greater the pressure difference at the outlet of the perforation section, the higher the plugging efficiency in the advantageous inlet section. Based on these results, the field construction of Well M was guided. The gas production was 142.66 × 104 m3/d after stimulation, and the production increase was significant. This study provides a theoretical basis for optimizing and designing the parameters of PDSTB in carbonate long horizontal wells.

On the adaptive deterministic block Kaczmarz method with momentum for solving large-scale consistent linear systems

The Kaczmarz method is a traditional and widely used iterative algorithm for solving large-scale consistent linear systems, while its improved block Kaczmarz-type methods have received much attention and research in recent years due to their excellent numerical performance. Hence, in this paper, we present a deterministic block Kaczmarz method with momentum, which is based on Polyak’s heavy ball method and a row selection criterion for a set of block-controlled indices defined by the Euclidean norm of the residual vector. The proposed method does not need to compute the pseudo-inverses of a row submatrix at each iteration and it adaptively selects and updates the set of block control indices, thus this is different from the block Kaczmarz-type methods that are based on projection and pre-partitioning of row indices. The theoretical analysis of the proposed method shows that it converges linearly to the unique least-norm solutions of the consistent linear systems. Numerical experiments demonstrate that the deterministic block Kaczmarz method with momentum method is more efficient than the existing block Kaczmarz-type methods.

The Use of Birth Ball as A Non-Pharmacological Complementary Therapy in The Reduction of Labor Pain in Phase 1

Childbirth is the process of expelling the fetus to the placenta, the process of giving birth is identical to pain, while to reduce this pain, non-pharmacological methods are carried out, one of which is the Birth Ball method. This study aims to evaluate the effectiveness of using birth ball as a non-pharmacological complementary therapy in reducing labor pain in the first stage. The method used was a narrative literature review by searching for relevant articles on Google Scholar using keywords such as “Birth ball” and “Labor pain”. Inclusion criteria included Indonesian-language articles published between 2021-2023. Of the six studies analyzed, it was found that birth ball use significantly reduced the intensity of labor pain. These studies showed that birth balls can accelerate cervical opening and reduce anxiety of laboring mothers through movements that increase endorphin release. In conclusion, birth balls are effective as an alternative method to reduce labor pain in Stage I, providing the added benefit of increasing maternal comfort and relaxation during the labor process. This study suggests the use of birth ball as part of midwifery practice to reduce labor pain non-pharmacologically.

Reliability-Based Robust Design Optimization with Fourth-Moment Method for Ball Bearing Wear

Ball bearings operating at low speeds and under heavy loads are susceptible to wear failure, leading to significant economic losses. The existing reliability-based robust design optimization method of the fourth-moment method has high accuracy and does not need to determine the random distribution of the input variables, but it is not possible to apply it to ball bearing wear due to the complexity of the bearing wear state function that cannot be characterized as an explicit form. To address this issue, this paper proposes a novel design method for ball bearing wear. Firstly, a surrogate model is constructed using the Kriging model method to establish a relationship between the bearing design parameters and the mechanical response. Subsequently, a wear reliability model is developed on the basis of the fourth-moment method, and reliability sensitivity analysis is conducted. Finally, the ball bearing wear reliability-based robust design optimization is accomplished through the use of a genetic algorithm. The results of the case calculations demonstrate that the proposed method effectively calculates the ball bearing wear reliability and analyzes the impact of design parameter randomness on reliability. Furthermore, optimizing the design parameters reduces the sensitivity of wear reliability to parameter randomness.

State Observer-Based Iterative Learning Control Design for Discrete Systems Using the Heavy Ball Method

State Observer-Based Iterative Learning Control Design for Discrete Systems Using the Heavy Ball Method

Mechanical milling promotes the preparation of catalyst lanthanum dodecyl sulfate and green solvent-free grinding for synthesis of N-heterocyclic derivatives

The lanthanum dodecyl sulfate catalyst (La(DS)3) was synthesized using a solvent-free mechanical ball method and applied in the preparation of solvent-free N-heterocyclic compounds. The preparation of the La(DS)3 catalyst and the synthesis of C-N bond series compounds only require brief ball milling of the mixed material at room temperature. Various analyses such as SEM, HRTEM, XRD, AFM, FT-IR, XPS, TGA, and DFT were conducted, which showed that the catalyst material synthesized by mechanical ball milling exhibited superior catalytic activity, thermal stability, and cyclic life compared to similar materials synthesized in an aqueous phase. The solvent-free catalytic synthesis of quinoxaline, dihydroacridin-1(2H)-one, and bis(indolyl)methanes derivatives achieved excellent target yields. Furthermore, the catalyst could be reused at least seven times without a significant decrease in activity after simple treatment. The catalyst also demonstrated gram scale scaling up in the model reaction. It exhibited weak hydrophilicity and a stable network-like layered nanostructure.

State Observer-Based Iterative Learning Control Design for Discrete Systems Using the Heavy Ball Method

The paper considers a state observer-based iterative learning control design problem for discrete linear systems. To accelerate the convergence of the learning error, a combination of the heavy ball method from optimization theory and the vector Lyapunov function method for a class of two-dimensional systems known as repetitive processes is used to develop a new design. A supporting numerical example is given, including a comparison with an existing design.

Impacts of CO2-CH4 Mixed Gas on Property of Formation Oil from the Bohai Oilfield

Mechanism analysis and technical scheme optimization on CO2 displacement and CO2 storage are based on the high-pressure physical properties of CO2-added formation oil. Oil and natural gas samples from the BZ25-1 block in the Bohai oilfield were used to conduct high-pressure physical property experiments to explore the impacts of CO2-CH4 mixed gas on the properties of formation oil. After injecting different amounts of mixed gas, the saturated pressure was measured by constant mass expansion test, the viscosity was measured by falling ball method, the expansion coefficient was measured by gas injection expansion test, and the gas–oil ratio and volume coefficient were obtained by single degassing test. The results show that with gas injection, the saturation pressure and dissolved gas–oil ratio of formation oil increase, the volume coefficient and expansion factor go up, while the oil viscosity reduces. With the increase in gas addition, the properties of formation oil continue to improve, but the increase in improvement becomes flat. With the increase in pressure, the amount of dissolved gas in the formation oil will also increase. High-purity CO2 is more helpful to change the properties of formation oil, while the gas mixed with CH4 is more beneficial to elevate the formation energy. For the BZ 25-1 block, the gas injection amount of about 80 mol% is appropriate and the CO2 purity of 60% can well balance the oil properties improvement and the formation pressure elevation.

Doxorubicin Loaded Nano-Gel Preoperative Application Effect as Adjuvant Chemotherapy on Osteosarcoma

This paper aimed to observe the effect of adjuvant chemotherapy with adriamycin loaded nano-gel on osteosarcoma. 120 patients with osteosarcoma who visited the hospital from January 2018 to February 2022 were selected as control group and nano group by the red blue ball method. The control group received conventional doxorubicin combined with ifosfamide chemotherapy. The nano group was treated with doxorubicin loaded nano-gel as adjuvant chemotherapy before surgery. Both groups received limb salvage surgery. Serum alkaline phosphatase (ALP), lactate dehydrogenase (LDH), vascular endothelial growth factor (VEGF), and basic fibroblast growth factor (bFGF) were compared between two groups before, after, and 1 day after chemotherapy. Follow up records were kept for 12 months to obtain adverse reactions to chemotherapy, postoperative clinical efficacy, and progression free survival time (PFS). No significant difference existed in ALP, LDH, VEGF, and bFGF levels between two groups of patients before chemotherapy (P > 0.05). For the overall comparison, inter group, time, and interaction effects had statistical significance (P < 0.05). For the comparison of two groups, the average ALP, LDH, VEGF, and bFGF in the nano group were lower after chemotherapy. The incidence of grade III–IV adverse reactions in the nano group was 10% lower than the controlling group. The CR+PR rate in the nano group was higher. The preoperative application of adriamycin loaded nano-gel as adjuvant chemotherapy can make the patients’ prognosis with osteosarcoma improved. It can enhance the chemotherapy effect, control the degree of adverse reactions of chemotherapy, and improve the clinical efficiency, thus extending the progression free survival period of patients with osteosarcoma.

Numerical simulation of aircraft lightning attachment zone using the enclosing ball method

The initial stage in aircraft lightning protection design and safety certification involves delineating the lightning attachment zone. The lightning leader’s development is inherently random, favoring the shortest path to the aircraft fuselage. In response, we employ the enclosing ball method to establish the lightning attachment zone. First, define the center point of the aircraft as the coordinate position for the sphere’s center, creating a sphere with a specified radius. The leader’s initial position is then selected from any point on the sphere. Second, by calculating distances between the leader’s position and various areas on the aircraft surface, we determine the shortest path. The corresponding aircraft surface area along this path is identified as the lightning attachment zone for the leader. Subsequently, choose a new leading position on the sphere and iterate through the calculation process until all sphere positions are considered. Finally, tally the occurrence frequencies for all calculated attachment areas, representing the attachment probability of each area based on its frequency of occurrence. This paper not only compares our method with the electrostatic field simulation method but also contrasts it with the probability distribution of lightning attachment points obtained from aircraft flight experiments. The comparison results are highly favorable, providing robust verification for the correctness of our approach.

Comparative Analysis of Viscosity Measurement Techniques Poiseuille Method versus Falling Ball Method

In fluid dynamics and related fields, accurately measuring liquid viscosity is vital. The traditional falling ball method, common in education and research, faces challenges in ensuring uniform fall and correcting for phenomena like eddy currents. This thesis introduces a new device based on the Poiseuille method, measuring viscosity through pressure difference and adjustable flow rates. Comparing it with the falling ball method, we found the latter has an average error of 5.21%, while the Poiseuille method has only 1.23%. The Poiseuille method avoids issues like Reynolds coefficient correction and inaccuracies from high ball speeds, offering stability and practical value.

CFD and Wind Tunnel Study on Cricket Ball at Different Seam Angle and Velocity

This study delves into the intriguing investigation of flow patterns over a cricket ball, employing both computational and experimental methods for a comparative analysis. The work explores about variation of velocities in different angles, here we have used as 4 cricket balls they are dukes cricket balls, SG cricket balls, dukes 3d printed cricket ball and SG printed cricket ball. While comparing all the cricket balls it shows values in the wind tunnel experiment in seam angles of 0°,30°,45°,60°& 90° in a subsonic wind tunnel. Both computational simulations and experimental observations were conducted to analyze the impact of seam angles and velocities on the cricket balls. The results obtained from computational models were successfully validated through experimental data, affirming the reliability of the computational approach in predicting aerodynamic characteristics. Flow visualization techniques further confirm these findings, highlighting the significance of keywords such as drag, seam angles, reverse swing, flow visualization, and computational fluid dynamics (CFD) in understanding the aerodynamics of cricket balls. Overall, this research provides valuable insights into optimizing bowling strategies by considering the interaction between seam angles, velocities, and aerodynamic behavior of cricket balls. Keyword: Ball drag analysis, Reverse swing analysis, CFD analysis, Cricket ball analysis.

IoT-based viscometer fabrication using the falling ball method for laboratory applications

This study outlines the production procedure of internet of things (IoT)- enabled viscometers designed for laboratory use. These viscometers utilize photodiode sensors, lasers, and falling ball techniques. The system is equipped with a temperature sensor that is utilized to quantify the impact of temperature on viscosity. The temperature sensor’s characterization yielded a R-square value of 0.999. The photodiode and laser sensors are utilized to operate a timer within the system, ensuring precise time measurement. The R-square value for the sensor characterization is 0.996. A viscometer equipped with an integrated IoT module for seamless wireless transmission of data. The photodiode timer sensor has an accuracy of 95.76% and a precision of 99.96%, while the temperature sensor has an accuracy of 99.43% and a precision of 99.93%. The viscometer transmits the measured viscosity data to the server using wireless technology. This IoT viscometer has the potential to enhance the efficiency and precision of liquid viscosity measurement in laboratory settings. Additionally, it enables real-time monitoring and data collection for subsequent analysis and research purposes.

Kekuatan Pembuktian Alat Bukti Keterangan Terdakwa Dalam Persidangan Online

law enforcement officers. Trials usually held face-to-face in the courtroom have changed to online via video conference due to the implementation of health protocols to maintain distance. The defendant and the defendant's legal advisor in several cases refused online trials. The problem in this research is the strength of evidence and legal certainty of the defendant's testimony in online trials. There are several things that form the basis, including the Criminal Procedure Code, criminal case evidence, criminal law evidentiary theory, legal certainty theory and online trials. This research chooses to use normative juridical research methods through a statutory approach (The Statute Approach). Legal materials come from secondary data collected using the Snow Balls Method and then sorted into primary, secondary and tertiary legal materials. The results of this research are that the evidence of the defendant's statement provided electronically has the same strength as an offline trial and the legal certainty of the defendant's statement in the online trial is guaranteed by statutory regulations. Online meetings provide an expanded interpretation of space that is not limited to direct physical face-to-face meetings but also face-to-face in cyber/virtual worlds, not limited by distance and place. The laws and regulations governing the Supreme Court provide space to establish Supreme Court Regulations to regulate Criminal Procedure Law when these provisions are not yet regulated in the Criminal Code.

Accelerated analysis on the triple momentum method for a two-layer ReLU neural network

The momentum method has become the workhorse in the deep learning community. To theoretical understand its success, researchers put efforts in demystifying its convergence properties when optimizing neural networks. For the convex problem, it is well-known that the triple momentum (TM) method owns the fastest theoretical convergence rate among all first-order methods. However, there exists no theoretical convergence results about the TM method in solving the non-convex neural networks training problem, let alone its acceleration guarantee. In this paper, we focus on the training process of the TM method for a two-layer ReLU neural network. Inspired by the accurate characterization of the high-resolution dynamical system, we consider the high-resolution ordinary differential equation (ODE) of the TM method. Under the over-parameterized assumption, we derive that the original non-convex optimization problem can be transformed to a strongly convex task. By applying an appropriate Lyapunov function, we prove that the TM method can linearly converge to a global minimum. Compared to the heavy ball method and Nesterov’s accelerated gradient method, our result provides the first guarantee for the acceleration of the TM method in training neural networks. Through empirical experiments, the accelerated convergence of the TM method and the effect of over-parameterization are validated.

Analysis of a Two-Step Gradient Method with Two Momentum Parameters for Strongly Convex Unconstrained Optimization

The paper is devoted to the theoretical and numerical analysis of the two-step method, constructed as a modification of Polyak’s heavy ball method with the inclusion of an additional momentum parameter. For the quadratic case, the convergence conditions are obtained with the use of the first Lyapunov method. For the non-quadratic case, sufficiently smooth strongly convex functions are obtained, and these conditions guarantee local convergence.An approach to finding optimal parameter values based on the solution of a constrained optimization problem is proposed. The effect of an additional parameter on the convergence rate is analyzed. With the use of an ordinary differential equation, equivalent to the method, the damping effect of this parameter on the oscillations, which is typical for the non-monotonic convergence of the heavy ball method, is demonstrated. In different numerical examples for non-quadratic convex and non-convex test functions and machine learning problems (regularized smoothed elastic net regression, logistic regression, and recurrent neural network training), the positive influence of an additional parameter value on the convergence process is demonstrated.