Splitting Procedure Research Articles

Three Representations of the Fractional p-Laplacian: Semigroup, Extension and Balakrishnan Formulas

Abstract We introduce three representation formulas for the fractional p-Laplace operator in the whole range of parameters 0 < s < 1 and 1 < p < ∞. Note that for p ≠ 2 this a nonlinear operator. The first representation is based on a splitting procedure that combines a renormalized nonlinearity with the linear heat semigroup. The second adapts the nonlinearity to the Caffarelli-Silvestre linear extension technique. The third one is the corresponding nonlinear version of the Balakrishnan formula. We also discuss the correct choice of the constant of the fractional p-Laplace operator in order to have continuous dependence as p → 2 and s → 0+, 1−. A number of consequences and proposals are derived. Thus, we propose a natural spectral-type operator in domains, different from the standard restriction of the fractional p-Laplace operator acting on the whole space. We also propose numerical schemes, a new definition of the fractional p-Laplacian on manifolds, as well as alternative characterizations of the W s, p (ℝ n ) seminorms.

A multilevel splitting algorithm for quick sampling

To reduce intermediate levels of splitting process and enhance sampling accuracy, a multilevel splitting algorithm for quick sampling is proposed in this paper. Firstly, the selected area of the elite set is expanded to maintain the diversity of the samples. Secondly, the combined use of an adaptive difference evolution algorithm and a local searching algorithm is proposed for the splitting procedure. Finally, a suite of benchmark functions are used for performance testing. The results indicate that the convergence rate and stability of this algorithm are superior to those of the classical importance splitting algorithm and an adaptive multilevel splitting algorithm.

Facile synthesis of highly efficient bifunctional electrocatalyst by vanadium oxysulfide spheres on cobalt-cobalt sulfonitride nanosheets for oxygen and hydrogen evolution reaction

Synthesis of efficient, low-cost, and stable bifunctional electrocatalysts with earth-abundant resources for electrochemical water electrolysis is a challenging subject for large-scale energy conversion processes. Herein, we report a high-performance electrocatalyst based on vanadium oxysulfide/cobalt-cobalt sulfonitride (VOS/Co-CoSN) for oxygen and hydrogen evolution reaction (OER and HER). The Co-CoSN film was synthesized on a copper sheet (CS) by a facile electrodeposition method. Then, VOS was electrochemically grown onto the Co-CoSN@CS electrode at various deposition times. At the optimal deposition time (300 s), the obtained VOS-300/Co-CoSN catalyst was studied for OER and HER in alkaline and acidic media, respectively. The binder free VOS-300/Co-CoSN@CS electrode showed significant improvement in catalytic activity towards both OER (Tafel slope of 0.201 V dec−1 with overpotential of 0.34 V @100 A m−2 current density in 1.0 M KOH media) and HER (Tafel slope of 0.048 V dec−1 with overpotential of 0.18 V@100 A m−2 current density in 0.5 M H2SO4 solution). Additionally, the electrocatalyst exhibited high durability and flexibility for both OER (98% stability after 24 h at 100 A m−2) and HER (99% stability after 12 h at 0.18 V vs.RHE) in alkaline and acidic conditions, respectively. The present work not only suggests a simple and single-step strategy for the synthesis of VOS-300/Co-CoSN nanostructure but also opens up a new avenue for the development of bendable and stable bifunctional, non-noble metal electrocatalysts towards both OER and HER through water splitting procedure.

Conservative semi-Lagrangian kinetic scheme coupled with implicit finite element field solver for multidimensional Vlasov Maxwell system

In this paper, a conservative semi-Lagrangian (CSL) kinetic scheme coupled with an implicit finite element method (IFEM) is developed for multidimensional electromagnetic plasma simulations. The present method (CSL-IFEM) enjoys the respective advantages of the CSL and IFEM, including mass conservation, high-order spatial accuracy, as well as being free from the Courant-Friedrichs-Lewy (CFL) condition. In present CSL-IFEM, the CSL scheme with a general high order positivity-preserving limiter is utilized for the spatial discretization of the Vlasov equation, which enables the proposed method to remove the CFL limitation in phase space, exactly conserve mass, and preserve the positivity of the distribution function. The IFEM solver is developed for the spatial discretization of the Maxwell equation, which makes the current method free from CFL limitation induced by the speed of light and easily handles general field boundary conditions. To make the proposed CSL-IFEM more efficient in multidimensional simulations, the dimensional splitting procedure and sparse matrix technology are implemented in CSL and IFEM, respectively. Then the Vlasov solver CSL and Maxwell solver IFEM are coupled via the current density calculated from the general Ohm law. Finally, several numerical experiments, including electromagnetic wave (2d0v), particle gyromotion (0d2v), streaming Weibel instability (1d2v) and magnetic reconnection (2d3v), are performed to demonstrate the capabilities of the proposed method.

Numerical analysis view on the general Trotter–Kato product formulae

We show that the abstract operator-theoretic (general) Trotter–Kato formulae yield the convergence of numerical methods used for solving differential equations. These methods combine operator splitting procedures with certain time discretisation schemes which should be consistent, strongly A-stable, positive rational approximations of the exponential function. We also show that it is possible to apply more numerical steps in one splitting time step and the convergence results remain true.

SPlit: An Optimal Method for Data Splitting

In this article, we propose an optimal method referred to as SPlit for splitting a dataset into training and testing sets. SPlit is based on the method of support points (SP), which was initially developed for finding the optimal representative points of a continuous distribution. We adapt SP for subsampling from a dataset using a sequential nearest neighbor algorithm. We also extend SP to deal with categorical variables so that SPlit can be applied to both regression and classification problems. The implementation of SPlit on real datasets shows substantial improvement in the worst-case testing performance for several modeling methods compared to the commonly used random splitting procedure.

Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows

Since proposed, the genuinely multidimensional Riemann solvers have been attracting more attentions because it considers the waves normal and parallel to the cell interfaces at the same time. However, all these methods are built upon the hyperbolic property of the compressible Euler equations. Therefore, they can not be applied to solve the Euler equations in steady subsonic cases which are with the elliptic property. In this study, a novel multidimensional Riemann solver called MULE-AUSMPWM (Multidimensional E-AUSMPW Modified) is proposed. It is built upon the Zha–Bilgen splitting procedure and adopts the Balsara's multidimensional wave model as the ME-AUSMPW scheme. In addition, it improves the ME-AUSMPW scheme's accuracy at subsonic speeds by avoiding simulating the convective fluxes in fully upwind manners. Extensive numerical tests, such as the two dimensional Euler problem, the one dimensional moving contact discontinuity case, the two-dimensional double Mach reflection case, the two-dimensional Riemann problem, and the turbulent flow past a 2d NACA0012 airfoil case, are conducted. Results illustrate that the MULE-AUSMPWM scheme proposed is capable of simulating compressible complex flows and improving the existing multidimensional Riemann solvers' accuracy at subsonic speeds remarkably.

Tunning of Templated CuWO4 Nanorods Arrays Thickness to Improve Photoanode Water Splitting.

The fabrication of the photoanode of the n-type CuWO4 nanorod arrays was successfully carried out through electrochemical deposition using anodic aluminum oxide (AAO) control templates and for the first time produced distinct gaps between the nanorod arrays. The effectiveness and efficiency of the resulting deposition was shown by the performance of the photoelectrochemical (PEC) procedure with a current density of 1.02 mA cm−2 with irradiation using standard AM 1.5G solar simulator and electron changed radiation of 0.72% with a bias potential of 0.71 V (vs. Ag/AgCl). The gap between each nanorod indicated an optimization of the electrolyte penetration on the interface, which resulted in the expansion of the current density as much as 0.5 × 1024 cm−3 with a flat band potential of 0.14 V vs. Ag/AgCl and also a peak quantum efficiency of wavelength 410 nm. Thus, also indicating the gaps between the nanorod arrays is a promising structure to optimize the performance of the PEC water splitting procedure as a sustainable energy source.

TEST COVERAGE ENHANCEMENT USING HYBRID MODULAR APPROACH FOR WEB BASED APPLICATION

Automation testing may be a process that compares the particular results to the specified outcome within the software application. Automation testing is one of the foremost effective ways to check web-based applications since it allows you to hide more scenarios in less time. Selenium is one every of the foremost popular and effective automation frameworks that have been widely used for automating the testing of applications. The modular testing framework is one of the techniques used for automated testing, in which test scripts are built by breaking down the entire application into smaller pieces. Multiple data sets cannot be used thanks to hardcoded data within the test scripts. In this paper, a hybrid approach of keyword-data driven strategy is presented, in which the test data and script are separated to allow for various datasets and greater coverage. Furthermore, for improved test coverage, this split procedure is used across many modules.

Transoral Parotidectomy.

Transoral parotidectomy allows for the management of parapharyngeal space tumors and accessory parotid gland tumors without the need for a transfacial/transparotid or mandible splitting procedure. It is a minimally invasive approach that permits a faster recovery and with a lesser risk of facial palsy.

Superior oblique split lengthening procedure for brown syndrome, outcomes and complications

IntroductionTo evaluate the outcomes of the superior oblique split tendon lengthening (SOSL) procedure for Brown syndrome (BS).MethodsAt a single institution, all patients who underwent SOSL surgery for BS from 2013...

A fully Eulerian solver for the simulation of multiphase flows with solid bodies: Application to surface gravity waves

In this paper a fully Eulerian solver for the study of multiphase flows for simulating the propagation of surface gravity waves over submerged bodies is presented. We solve the incompressible Navier–Stokes equations coupled with the volume of fluid technique for the modeling of the liquid phases with the interface, an immersed body method for the solid objects and an iterative strong–coupling procedure for the fluid–structure interaction. The flow incompressibility is enforced via the solution of a Poisson equation which, owing to the density jump across the interfaces of the liquid phases, has to resort to the splitting procedure of Dodd and Ferrante [1].The solver is validated through comparisons against classical test cases for fluid–structure interaction like migration of particles in a pressure–driven channel, multiphase flows, ‘water exit’ of a cylinder and a good agreement is found for all tests. Furthermore, we show the application of the solver to the case of a surface gravity wave propagating over a submerged reversed pendulum and verify that the solver can reproduce the energy exchange between the wave and the pendulum. Finally the three–dimensional spilling breaking of a wave induced by a submerged sphere is considered.

Bile Microbiota in Liver Transplantation: Proof of Concept Using Gene Amplification in a Heterogeneous Clinical Scenario.

Objective: Historically, bile in the biliary tract has been considered sterile. Most of the series are based on patients with biliary tract diseases or the bile has been obtained with procedures susceptible to contamination.Methods: We evaluated the bile in a heterogeneous cohort of liver donors and recipient patients, with samples obtained in a sterile way, directly from the gallbladder and the common bile duct.Results: We assessed the bile microbiota in six liver donors and in six liver recipients after whole or split liver procedures in adult or pediatric recipients. Bile samples were studied using PCR sequencing of the 16S ribosomal RNA gene amplification (rDNA).Conclusions: We demonstrated that the bile is sterile, thereby ruling this out as a source of contamination following transplant.

Pediatric split liver transplantation for congenital factor X deficiency: first 10-year follow-up of a case with portal vein stenting

Congenital factor X (FX) deficiency is a rare autosomal-recessive disease that induces bleeding disorder. Herein, we present the 10-year posttransplant course of a pediatric patient who underwent liver transplantation (LT) with portal vein (PV) stenting for correction of severe congenital FX deficiency, with focus on long-term maintenance of coagulation function and patency of PV stenting. A 17-month-old infant with recurrent hemorrhagic episodes due to FX deficiency underwent split LT using a left lateral section graft. The graft-recipient weight ratio was 2.2%. The graft implantation procedures were performed by following the standard pediatric split LT procedure. Nevertheless, a wall stent was inserted due to PV anastomotic stenosis on posttransplant day 1. Graft function recovered slowly because of partial parenchyma infarct, and the patient was discharged at 46 days after LT operation. The FX activity started to increase soon after LT and gradually normalized; the coagulation profiles have been maintained well for the past 10 years. The patient has been doing well for the past 10 years after LT without any episodes of abnormal bleeding. Due to the risk of vascular complications owed to PV stenting, life-long follow-up is mandatory with special attention until attainment of complete physical growth to adolescent and adulthood.

Superior oblique split tendon elongation for Brown's syndrome: Long-term outcomes.

To report the outcomes of superior oblique split tendon elongation in Brown's syndrome. Charts of 17 consecutive Brown's syndrome patients who underwent superior oblique split tendon elongation were reviewed and clinical data regarding preoperative, intraoperative, and postoperative data were collected. About 17 eyes of 17 children with congenital Brown's syndrome underwent superior oblique split tendon elongation between January 2012 and March 2020 by a single surgeon. Mean age at surgery was 5.47 ± 2.82 (range 1.50-13.2). Eight (47.1%) were female. Preoperative deficit of elevation in adduction was -4 in all children. At the end of surgery, all eyes were freely elevated on adduction, on forced duction test. Mean follow-up time of 26.24 ± 11.22 (range 11-53) months. In 15 of 17 children (88.2%), motility improved, orthotropia in primary position was achieved, and head posture eliminated (p < 0.001). Superior oblique palsy occurred in two children, who after reoperation, achieved an acceptable outcome. No intraoperative complications were recorded. The superior oblique split tendon elongation procedure is a useful surgical technique with stable and satisfying outcomes for the treatment of severe congenital Brown's syndrome.

A REVIEW ON THE DIVISION OF MAGNETIC RESONANT PROSTATE IMAGES WITH DEEP LEARNING

Deep learning; it is often used in dividing processes on images in the biomedical field. In recent years, it has been observed that there is an increase in the division procedures performed on prostate images using deep learning compared to other methods of image division. Looking at the literature; It is seen that the process of dividing prostate images, which are carried out with deep learning, is an important step for the diagnosis and treatment of prostate cancer. For this reason, in this study; to be a source for future splitting operations; deep learning splitting procedures on prostate images obtained from magnetic resonance (MRI) imaging devices were examined. Key words: deep learning, image division, prostate cancer

Enhanced photocatalytic overall water splitting via MOF-derived tetragonal BiVO4-based solid solution

In this work, BiVO4-based solid solutions, Bi0.5Y0.5VO4, were prepared via the MOF-derived method initially. The physical and chemical properties of the Bi0.5Y0.5VO4 samples were characterized by XRD, Raman spectra, XPS, HRTEM, element mapping, UV–vis DRS spectrum, TRPL and electrochemical analysis. The results showed that Y sources will be beneficial for the generation of tetragonal phase BiVO4, which made Bi0.5Y0.5VO4 samples constructed by tetragonal Bi0.5Y0.5VO4 and amorphous Bi0.5Y0.5VO4. The ratio of the tetragonal Bi0.5Y0.5VO4 was changed if the variation of the calcined time increased, which could be ascribed to the conversion of the amorphous Bi0.5Y0.5VO4. Consequently, photocatalytic overall water splitting property was enhanced and the results exhibited that Bi0.5Y0.5VO4-10 h samples exhibited the best performance with a rate of 124.2 μmol H2 and 61.7 μmol O2 per hour. The reason could be attributed to the variation of twisting degree, which thus influencing the internal electric field of the materials. More importantly, after metallic Pt particles as co-catalysts deposited, the ratio of H2:O2 was decreased. It could be proposed that the electric field shield effect will emerge to regulate the interfacial internal electric field further, which could play an essential role in the procedure of photocatalytic water splitting, especially for the reduction procedure.

Future-proof Radiation therapist (RTT) practice in a pandemic - Lessons learnt from COVID-19.

The European SocieTy for Radiotherapy and Oncology Radiation Therapist Committee (ESTRO RTTC) published a guidance document and infographic providing recommendations to minimise risk of COVID-19 transmission in radiotherapy (RT) departments. The purpose of this study was to investigate the changes embedded in RT practice in the COVID-19 era and to recommend proactive measures to protect RT practice in future pandemics. The study was initiated by the ESTRO Radiation Oncology Safety and Quality Committee (ROSQC). A survey consisting of multiple choice, open ended and Likert scale questions was created to analyse the extent of changes embedded in RT practice in response to the COVID-19 pandemic under the four domains: patient care, RTT workflow, remote working and RT practice. This online survey was distributed globally in May 2020. 229 respondents across 27 countries completed the survey. 60% of respondents reported continuing/commencing RT in COVID-19 patients. Routine testing of patients and RTTs was not common. Split teams' procedures, hot linacs and separate entrances were implemented by 50% of respondents. Remote working was implemented for RT team members where face to face patient contact was not essential. Lack of staff, connectivity issues and lack of confirmed positive cases in the department were the main reasons cited for not implementing recommended measures. It is suggested that RT departments have responded to the COVID-19 pandemic and implemented certain changes in RT practice. RT departments should act now to implement recommended proactive measures to protect patients and RTTs - frontline healthcare workers.

Ex Situ Dual Hypothermic Oxygenated Machine Perfusion for Human Split Liver Transplantation.

After transport using static cold storage, a 51-year-old brain death donor liver underwent end-ischemic DHOPE. During DHOPE, the donor liver was maintained <10 °C and oxygenated with a Po2 of >106 kPa. An ex situ ERL/LLS split was performed with continuing DHOPE throughout the procedure to avoid additional ischemia time. Total cold ischemia times for the LLS and ERL were 205 minutes and 468 minutes, respectively. Both partial grafts were successfully transplanted at 2 different transplant centers. Peak aspartate aminotransferase and alanine aminotransferase were 172 IU/L and 107 IU/L for the LLS graft, and 839 IU/L and 502 IU/L for the ERL graft, respectively. The recipient of the LLS experienced an episode of acute cellular rejection. The ERL transplantation was complicated by severe acute pancreatitis with jejunum perforation requiring percutaneous drainage and acute cellular rejection. No device-related adverse events were observed. Liver splitting during continuous DHOPE preservation is feasible, has the potential to substantially shorten cold ischemia time and may optimize transplant logistics. Therefore liver splitting with DHOPE can potentially improve utilization of split liver transplantation.

EVALUATION OF INTERCHANGEABLE GUIDE IN MINIMALLY INVASIVE RIDGE SPLITTING WITH SIMULTANEOUS IMPLANT PLACEMENT (A PROSPECTIVE CLINICAL STUDY)

Background: The conventional ridge splitting technique offers a feasible and more consistent approach for the challenging narrow alveolar ridge. However, this entails raising of a complete flap to allow an adequate visibility of the osseous defect resulting in disturbance of vascular supply and risk of bone resorption. Stereolithography helps the manufacture of surgical guides using 3D generated models for an accurate placement of implants with minimal invasiveness thus preserving the periosteum. Objectives: To assess the precision of dental implant placement in narrow ridges after ridge splitting minimally invasive technique using an interchangeable guide. Materials and Methods: A prospective study was including 5 patients with anterior maxillary narrow ridge. All patients were selected to suit the proposed inclusion and exclusion criteria. Ridge split procedure was performed for all selected subjects assisted with the surgical guide with simultaneous placement of implants. Patients were evaluated by clinical and radiographical assessments with an average of 6 months follow up. Results: 8 implants were placed. Angular deviations with an average of 2.61 ± 1.46 degrees. The mean values of the horizontal deviation at the coronal and apex sides of the implant were 0.70 ± 0.46 mm and 0.98 ± 0.35 mm. While the Vertical deviations (V) with an average of 0.39 ± 0.29 mm. There were statistically significant differences between preoperative, immediate postoperative and 6 months postoperative values of bone width and density. Conclusions: Alveolar ridge split technique assisted with an interchangeable surgical guide is a feasible and reliable method for placement of dental implants