Circle Method Research Articles

Estimates for Smooth Weyl Sums on Major Arcs

Abstract We present estimates for smooth Weyl sums of use on sets of major arcs in applications of the Hardy–Littlewood method. In particular, we derive mean value estimates on major arcs for smooth Weyl sums of degree $k$ delivering essentially optimal bounds for moments of order $u$ whenever $u>2\lfloor k/2\rfloor +4$.

Asymptotics of parity biases for partitions into distinct parts via Nahm sums

AbstractFor a random partition, one of the most basic questions is: what can one expect about the parts that arise? For example, what is the distribution of the parts of random partitions modulo ? As most partitions contain a 1, and indeed many 1s arise as parts of a random partition, it is natural to expect a skew toward . This is indeed the case. For instance, Kim, Kim, and Lovejoy recently established “parity biases” showing how often one expects partitions to have more odd than even parts. Here, we generalize their work to give asymptotics for biases for partitions into distinct parts. The proofs rely on the Circle Method and give independently useful techniques for analyzing the asymptotics of Nahm‐type ‐hypergeometric series.

A note on Diophantine inequalities in function fields

We will discuss how the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn circle method can be used to study $\mathbb{F}_q[t]$ solutions to inequalities of the form \[\mathrm{ord}(\lambda_1p_1^k+\cdots+\lambda_sp_s^k-\gamma)<\tau , \] where constants $\lambda_1,\dots, \lambda_s \in\mathbb{F}_q((1/t))$ satisfy certain conditions. This result is a generalization of the work done by Spencer in [11] to count the number of solutions to inequalities of the form \[\mathrm{ord}(\lambda_1p_1^k+\cdots+\lambda_sp_s^k)<\tau.\]

Analysis of Surface Texture of Asphalt Mixture with Sand Circle Method

A road is usually defined as an infrastructure connecting a zone to other zones. As service and safety are essential for vehicle users, any conditions related to the pavement, including surface texture, are considered. The importance of this matter is that many researchers or practitioners are concerned with the quality of asphalt mixtures, whether structural or functional, which affect the safety and security of road users, mainly related to the texture of the pavement surface. This research aims to determine the texture depth (MTD, Mean Texture Depth). The research method used is the circle sand method, which is tested using the Sand Patch tool. The asphalt mixture type uses AC-WC with a composition of 39% coarse aggregate, 54.5% fine aggregate, and 6.5% filler. Optimum Asphalt Content of 6.28% and Density of 2.28 were obtained, and texture depth of 0.549 mm was more significant than 0.45 mm (Bina Marga 2010 revision 3). The conclusion is based on the design composition of the aggregate mix in the AC-WC asphalt mixture, which has a safe texture.

Integral points on a del Pezzo surface over imaginary quadratic fields

Chambert-Loir and Tschinkel constructed a framework for a geometric interpretation of the density of integral points on certain varieties, which was refined by Wilsch. By using harmonic analysis and the circle method, it was proved for some partial equivariant compactifications of vector groups over arbitrary number fields and high-dimensional complete intersections over Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document}. Further, there are some examples of using the torsor method for singular del Pezzo surfaces over Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document}. In this paper, we generalise the torsor method for integral points from Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document} to imaginary quadratic number fields. As a first representative example, we characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type A3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{A}}_3$$\\end{document} over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these integral points of bounded height by using universal torsors and interpret the count geometrically to prove an analogue of Manin’s conjecture for the set of integral points with respect to the singularity and to a line. Our results coincide with the predicted framework.

Non-nematicity of the filamentary phase in systems of hard minor circular arcs.

This work further investigates an aspect of the phase behavior of hard circular arcs whose phase diagram has been recently calculated by Monte Carlo numerical simulations: the non-nematicity of the filamentary phase that hard minor circular arcs form. Both second-virial density-functional theory and further Monte Carlo numerical simulations find that the positional one-particle density function undulates in the direction transverse to the axes of the filaments while further Monte Carlo numerical simulations find that the mobility of the hard minor circular arcs across the filaments occurs via a mechanism reminiscent of the mechanism of diffusion in a smectic phase: the filamentary phase is not a {"modulated" ["splay(-bend)"]} nematic phase.

Analysis on the derivative of the discriminant polynomial for the critical almost Mathieu operator

This article first introduces the discriminant polynomial and the central spectral band of the critical almost Mathieu operator. The Hardy–Littlewood method and the symbolic coding of continued fractions are introduced and applied to estimate the first-order and the second-order derivatives of the discriminant polynomial. Finally, these results are applied to obtain a lower bound for the measure of the central spectral band.

Calculation Method for the Loose Circle of Tunnel-Surrounding Rock Considering the Strain-Softening Effect

Calculation Method for the Loose Circle of Tunnel-Surrounding Rock Considering the Strain-Softening Effect

Superhydrophobic and antibacterial larch wood prepared by PEI controlled growth of conical ZnO nanopillar

The natural antibacterial performance of cicada wings inspired the morphology design and application of zinc oxide (ZnO) nanoparticles on wood surfaces to enhance combined antibacterial function. The commonly interior used larch wood was chosen as base material and firstly pre-treated with ultrasonic-hydrothermal method, the deposition of ZnO nanoparticles with different morphologies was controlled by polyethyleneimine (PEI) concentration during the crystal growth, and the analysis of surface characteristics and antibacterial efficacy was fully tested. Scanning Electron Microscopy (SEM) observations revealed that the addition of PEI altered the morphology of ZnO nanoparticles on the wood surface. ZnO structures without PEI exhibited hexagonal prismatic shapes. As the PEI concentration increased, the particle size of ZnO decreased. When 6 mmol/L of PEI was added, ZnO transformed into a conical structure. Contact angle measurements confirmed the preparation of superhydrophobic ZnO, which exhibited self-cleaning properties. The antibacterial circle method test results showed that superhydrophobic ZnO wood prepared with 6 mmol/L of PEI exhibited superior antibacterial properties, with higher activity against Staphylococcus aureus compared to Escherichia coli. Overall, the study demonstrates a promising approach to developing polyfunctional and effective antibacterial wood surfaces inspired by natural cicada wings nanostructures.

Assessing the current role of AP and Bernageau view radiographs in measurement of glenoid bone loss in patients with recurrent shoulder dislocation: correlation with computed tomography, magnetic resonance imaging, and arthroscopy.

Evaluation of glenoid bone loss following recurrent anterior shoulder dislocations is normally performed using cross sectional imaging. To assess how anteroposterior (AP) and Bernageau view radiographs compare to computed tomography (CT), magnetic resonance imaging (MRI) and arthroscopy for evaluating glenoid bone loss in patients with recurrent anterior shoulder dislocation. A prospective observational study was performed on 32 patients over two years at a tertiary orthopedic center. The loss of sclerotic glenoid rim (LSGL) on AP radiograph and the percentage relative glenoid bone loss on the Bernageau radiograph were assessed. The percentage glenoid bone loss and anterior straight line (ASL) were calculated using a best fit en face circle method using CT and MRI. Percentage glenoid bone loss was also calculated during arthroscopy in multiples of 5%. In our study, 90.6% (29) patients were males, while only 9.4% (3) were females. This can be attributed to the involvement of the males in outdoor activities and sports. Also, the maximum number of patients were found to belong to 21-30years of age, with the mean age being 28.66years. Of the 32 patients, loss of sclerotic glenoid line (LSGL) on AP radiographs correlated with glenoid bone loss on cross-sectional imaging in 27 patients. Three patients had equivocal LSGL and 2 patients with glenoid bone loss on CT did not demonstrate LSGL. The difference between the two modalities was not statistically significant (p value = 0.002). The glenoid bone loss on Bernageau view correlated with glenoid bone loss on cross sectional imaging in all but one patient. The bone loss as evaluated by radiograph Bernageau view was found to have strong correlation (correlation coefficient r = 0.948, p value < 0.0001). AP and Bernageau radiographic views for anterior shoulder dislocations demonstrate good correlation with glenoid bone loss on cross-sectional imaging. They may also be used as an adjunct to predict overall bone loss on CT and at arthroscopy.

Gentrification as a field of study in environmental sciences

This article examines the interaction between gentrification and environmental sciences in Colombia, using a hermeneutic desk review approach to unravel how this urban phenomenon influences and is influenced by environmental factors. Through the hermeneutic circle method, adapted for a single researcher, a deep understanding of the existing literature is achieved and main lines of research are identified. Areas explored include green gentrification, climate change impacts, health and well-being effects, environmental justice, and associated public policies. The study highlights the need for policies that balance environmental improvement with social protection, and underlines the importance of including local communities in urban planning processes to prevent displacement and increase social equity. This interdisciplinary approach provides valuable insights to understand the complexity of gentrification and its multiple dimensions in an urban and environmental context

A morphological indicator for aortic dissection: fitting circle of the thoracic aorta

BackgroundThis study aims to identify a morphological indicator of aortic dissection (AD) based on the geometrical characteristics of the thoracic aorta.MethodsWe evaluated computed tomographic angiograms of 63 samples with AD (22 with type A AD, 41 with type B AD) and 71 healthy samples. Via centerline extraction and spatial transformation, the spatial entanglement of the aorta was minimized, and the expanded 2D aortic morphology was obtained. The 2D morphology of the thoracic aorta was fit to a circle. The applicability of the fitting circle method for identifying aortic dissection was verified by multivariable logistic regression analysis.ResultsVia the 3D coordinate transformation algorithm, the optimal aortic view was obtained. On this view, the geometrical characteristics of the thoracic aortas of the healthy controls were similar to a portion of a circle (sum of residuals: 3502.45 ± 2566.71, variance: 86.23 ± 56.60), while that of AD samples had poorer similarity to the circle (sum of residuals: 5404.78 ± 3891.69, variance: 129.90 ± 90.09). This difference was significant (p < 0.001). A logistic regression model showed that increased deformation of the thoracic aorta was a significant indicator of aortic dissection (odds ratio: 1.35, p = 0.034).ConclusionsThe morphology of the healthy thoracic aorta could be fit to a circle, while that of the dissected aorta had poorer similarity to the circle. The statistics of the circle are an effective indicator of aortic deformation in AD.Trial registrationThis study is registered in the Chinese Clinical Trial Registry (ChiCTR2000029219).

Sums of singular series along arithmetic progressions and with smooth weights

Sums of the singular series constants that appear in the Hardy–Littlewood [Formula: see text]-tuples conjectures have long been studied in connection to the distribution of primes. We study constrained sums of singular series, where the sum is taken over sets whose elements are specified modulo [Formula: see text] or weighted by smooth functions. We show that the value of the sum is governed by incidences modulo [Formula: see text] of elements of the set in the case of arithmetic progressions and by pairings of the smooth functions in the case of weights. These sums shed light on sums of singular series in other formats.

Quality Control Analysis of Bath Soap Products With Quality Control Circle (QCC) Method At Alliance Consumer Products Indonesia Uses to Minimize Failed Products

Quality Control Analysis of Bath Soap Products With Quality Control Circle (QCC) Method At Alliance Consumer Products Indonesia Uses to Minimize Failed Products

Precise and efficient measurement of tibial slope on magnetic resonance imaging (MRI): two novel autonomous pipelines by traditional and deep learning algorithms.

The measurement of posterior tibial slopes (PTS) can aid in the screening and prevention of anterior cruciate ligament (ACL) injuries and improve the success rate of some other knee surgeries. However, the circle method for measuring PTS on magnetic resonance imaging (MRI) scans is challenging and time-consuming for most clinicians to implement in practice, despite being highly repeatable. Currently, there is no automated measurement scheme based on this method. To enhance measurement efficiency, consistency, and reduce errors resulting from manual measurements by physicians, this study proposes two novel, precise, and computationally efficient pipelines for autonomous measurement of PTS. The first pipeline employs traditional algorithms with experimental parameters to extract the tibial contour, detect adhesions, and then remove these adhesions from the extracted contour. A cyclic process is employed to adjust the parameters adaptively and generate a better binary image for the following tibial contour extraction step. The second pipeline utilizes deep learning models for classifying MRI slice images and segmenting tibial contours. The incorporation of deep learning models greatly simplifies the corresponding steps in pipeline 1. To evaluate the practical performance of the proposed pipelines, doctors utilized MRI images from 20 patients. The success rates of pipeline 1 for central, medial, and lateral slices were 85%, 100%, and 90%, respectively, while pipeline 2 achieved success rates of 100%, 100%, and 95%. Compared to the 10 minutes required for manual measurement, our automated methods enable doctors to measure PTS within 10 seconds. These evaluation results validate that the proposed pipelines are highly reliable and effective. Employing these tools can effectively prevent medical practitioners from being burdened by monotonous and repetitive manual measurement procedures, thereby enhancing both the precision and efficiency. Additionally, this tool holds the potential to contribute to the researches regarding the significance of PTS, particularly those demanding extensive and precise PTS measurement outcomes.

Role of CT Scan in Preoperative Evaluation of Bone Loss in Anterior Shoulder Instability Using the On Track and Off Track Concept

Abstract Purpose The purpose of this study was to assess the role of CT scan in preoperative evaluation of glenoid and humeral head bone loss in cases of recurrent anterior shoulder joint dislocation using on track and off track concept and whether it can be used to predict engagement during arthroscopy. Patients and Methods In the period from June 2019 to October 2022, this study was conducted in Ain Shams University hospitals including 40 cases with recurrent anterior shoulder dislocation. CT scan with 3D reconstruction was done to calculate the width of the glenoid track using the best fit circle method as well as the Hill Sachs interval. We used the on-track off-track method to predict engagement and these results were compared with the findings related to engagement seen during arthroscopy Results Using the on-track /off-track technique on CT images, 22 of the 25 engaging (off-track) lesions was predicted correctly (sensitivity, 88%).While 13 of the 15 cases that did not engage (on-track) was correctly predicted (specificity, 86.7%). Overall, the accuracy of the on-track off-track method was 87.5% with a positive predictive value (PPV) of 91.7% and negative predictive value (NPV) of 81.3%. The on-track /off-track method was found to be a significant predictor of engagement as there is no statistically significant difference (p = 0.18) between this method and arthroscopic findings. Conclusion Our study showed that using the on-track off-track method by CT scan can accurately assess the glenoid and humeral head bone losses seen in patients with anterior shoulder instability for predicting the presence of engagement, or off-track, lesions. This technique can be used for preoperative evaluation to help in deciding the type of surgical procedure performed on patients with anterior shoulder instability.

Experimental and Engineering Simulation of Loss Characteristics of Silicon Steel Wafers Based on Levenberg-Marquardt Optimization Algorithm

Abstract The loss characteristics of 20WTG1500 silicon steel wafers are simulated and studied by using the Epstein square circle method. First, the loss-measured data are fitted based on the classical Bertotti loss model. When working, a Levenberg-Marquardt (L-M) algorithm is proposed to calculate the parameters of the loss model accurately. For the problem of significant calculation errors of hysteresis loss and stray loss in the classical loss separation model, a variable parameter closely related to the magnetic induction intensity is constructed by using the fixed parameter values of the classical loss model. Then, the loss improvement model is proposed. The accuracy of the improved model is proved by comparing the fitting results of the enhanced model with the measured data.

On Some Multipliers Related to Discrete Fractional Integrals

This paper explores the properties of multipliers associated with discrete analogues of fractional integrals, revealing intriguing connections with Dirichlet characters, Euler’s identity, and Dedekind zeta functions of quadratic imaginary fields. Employing Fourier transform techniques, the Hardy–Littlewood circle method, and a discrete analogue of the Stein–Weiss inequality on product space through implication methods, we establish ℓp→ℓq bounds for these operators. Our results contribute to a deeper understanding of the intricate relationship between number theory and harmonic analysis in discrete domains, offering insights into the convergence behavior of these operators.

ANALISIS PENGENDALIAN KUALITAS UNTUK MENGURANGI DEFECT PADA GLASS BOTTLE DENGAN MENGGUNAKAN METODE QUALITY CONTROL CIRCLE PT MULIAGLASS CONTAINER DIVISION CIKARANG JAWA BARAT

PT Muliaglass Container Division is a subsidiary of PT Mulia Industrindo, Tbk which is engaged in the glass industry by producing flat glass, glass block, glass packaging, and automotive safety glass as a result of its production. PT Muliaglass Container Division was founded in 1989. The quality control carried out by PT Muliaglass Container Division experienced problems in the Quality Control section or checking checkers, resulting in the defect pass rate so far exceeding the tolerance limits set by the company. There are several types of product defects in glass bottle packaging at PT Muliaglass Container Division, namely Check Ring, Check Under Ring, Leaner, Hot Mold Check, and others. To overcome the problems encountered, research is needed using the Quality Control Circle Method and Statistical Quality Control which are used to calculate how big the reasonable limit is in the product pass rate. After processing Statistical Quality Control data and knowing the number of acceptable quality labels for passing controlled defects or not, proceed with the Quality Control Circle Method, to find out what causes product defects to pass.

The circle method and shifted convolution sums involving the divisor function

Let Q(x) be a positive definite integral quadratic form with the determinant D being squarefree, and r(n,Q) denote the number of representations of n by the quadratic form Q. In this paper, we apply the Hardy-Littlewood-Kloosterman circle method to derive the asymptotic formula for the shifted convolution sum of the divisor function d(n) and Fourier coefficients r(n,Q). With more efforts, our method should have a number of applications for other multiplicative functions.