Design of Pinion Machine Tool-settings for Spiral Bevel Gears by Controlling Contact Path and Transmission Errors

This paper proposes a new approach to design pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. It is based on the satisfaction of contact condition of three given control points on the tooth surface. The three meshing points are controlled to be on a predesigned straight contact path that meets the pre-designed parabolic function of transmission errors. Designed separately, the magnitude of transmission errors and the orientation of the contact path are subjected to precise control. In addition, in order to meet the manufacturing requirements, we suggest to modify the values of blank offset, one of the pinion machine tool-settings, and redesign pinion ma- chine tool-settings to ensure that the magnitude and the geometry of transmission errors should not be influenced apart from minor effects on the predesigned straight contact path. The proposed approach together with its ideas has been proven by a numerical example and the manufacturing practice of a pair of spiral bevel gears.

Uncertainties of landslide susceptibility prediction: Influences of random errors in landslide conditioning factors and errors reduction by low pass filter method

In the existing landslide susceptibility prediction(LSP)models,the influences of random errors in landslide conditioning factors on LSP are not considered,instead the original conditioning factors are directly taken as the model inputs,which brings uncertainties to LSP results.This study aims to reveal the influence rules of the different proportional random errors in conditioning factors on the LSP un-certainties,and further explore a method which can effectively reduce the random errors in conditioning factors.The original conditioning factors are firstly used to construct original factors-based LSP models,and then different random errors of 5%,10%,15% and 20%are added to these original factors for con-structing relevant errors-based LSP models.Secondly,low-pass filter-based LSP models are constructed by eliminating the random errors using low-pass filter method.Thirdly,the Ruijin County of China with 370 landslides and 16 conditioning factors are used as study case.Three typical machine learning models,i.e.multilayer perceptron(MLP),support vector machine(SVM)and random forest(RF),are selected as LSP models.Finally,the LSP uncertainties are discussed and results show that:(1)The low-pass filter can effectively reduce the random errors in conditioning factors to decrease the LSP uncertainties.(2)With the proportions of random errors increasing from 5%to 20%,the LSP uncertainty increases continuously.(3)The original factors-based models are feasible for LSP in the absence of more accurate conditioning factors.(4)The influence degrees of two uncertainty issues,machine learning models and different proportions of random errors,on the LSP modeling are large and basically the same.(5)The Shapley values effectively explain the internal mechanism of machine learning model predicting landslide sus-ceptibility.In conclusion,greater proportion of random errors in conditioning factors results in higher LSP uncertainty,and low-pass filter can effectively reduce these random errors.

Self-calibration and Compensation of Setting Errors for Surface Profile Measurement of a Microstructured Roll Workpiece

Microstructured roll workpieces have been widely used as functional components in the precision industries. Current researches on quality control have focused on surface profile measurement of microstructured roll workpieces, and types of measurement systems and measurement methods have been developed. However, low measurement efficiency and low measurement accuracy caused by setting errors are the common disadvantages for surface profile measurement of microstructured roll workpieces. In order to shorten the measurement time and enhance the measurement accuracy, a method for self-calibration and compensation of setting errors is proposed for surface profile measurement of microstructured roll workpieces. A measurement system is constructed for the measurement, in which a precision spindle is employed to rotate the roll workpiece and an air-bearing displacement sensor with a micro-stylus probe is employed to scan the microstructured surface of the roll workpiece. The resolution of the displacement sensor is 0.14 nm and that of the rotary encoder of the spindle was 0.15r~. Geometrical and mathematical models are established for analyzing the influences of the setting errors of the roll workpiece and the displacement sensor with respect to the axis of the spindle, including the eccentric error of the roll workpiece, the offset error of the sensor axis and the zero point error of the sensor output. Measurement experiments are carded out on a roll workpiece on which periodic microstructures are a period of 133 i^m along the circumferential direction. Experimental results demonstrate the feasibility of the self-compensation method. The proposed method can be used to detect and compensate the setting errors without using any additional accurate artifact.

Prevalence of visual impairment and estimation of refractive errors among school children in Kakamega,Kenya

AIM:To investigate the prevalence of visual impairment(VI)and provide an estimation of uncorrected refractive errors in school-aged children,conducted by optometry students as a community service.METHODS:The study was cross-sectional.Totally 3343 participants were included in the study.The initial examination involved assessing the uncorrected distance visual acuity(UDVA)and visual acuity(VA)while using a+2.00 D lens.The inclusion criteria for a subsequent comprehensive cycloplegic eye examination,performed by an optometrist,were as follows:a UDVA<0.6 decimal(0.20 logMAR)and/or a VA with+2.00 D≥0.8 decimal(0.96 logMAR).RESULTS:The sample had a mean age of 10.92±2.13y(range 4 to 17y),and 51.3%of the children were female(n=1715).The majority of the children(89.7%)fell within the age range of 8 to 14y.Among the ethnic groups,the highest representation was from the Luhya group(60.6%)followed by Luo(20.4%).Mean logMAR UDVA choosing the best eye for each student was 0.29±0.17(range 1.70 to 0.22).Out of the total,246 participants(7.4%)had a full eye examination.The estimated prevalence of myopia(defined as spherical equivalent≤-0.5 D)was found to be 1.45%of the total sample.While around 0.18%of the total sample had hyperopia value exceeding+1.75 D.Refractive astigmatism(cil<-0.75 D)was found in 0.21%(7/3343)of the children.The VI prevalence was 1.26%of the total sample.Among our cases of VI,76.2%could be attributed to uncorrected refractive error.Amblyopia was detected in 0.66%(22/3343)of the screened children.There was no statistically significant correlation observed between age or gender and refractive values.CONCLUSION:The primary cause of VI is determined to be uncorrected refractive errors,with myopia being the most prevalent refractive error observed.These findings underscore the significance of early identification and correction of refractive errors in school-aged children as a means to alleviate the impact of VI.

Uncertainties in landslide susceptibility prediction:Influence rule of different levels of errors in landslide spatial position

The accuracy of landslide susceptibility prediction(LSP)mainly depends on the precision of the landslide spatial position.However,the spatial position error of landslide survey is inevitable,resulting in considerable uncertainties in LSP modeling.To overcome this drawback,this study explores the influence of positional errors of landslide spatial position on LSP uncertainties,and then innovatively proposes a semi-supervised machine learning model to reduce the landslide spatial position error.This paper collected 16 environmental factors and 337 landslides with accurate spatial positions taking Shangyou County of China as an example.The 30e110 m error-based multilayer perceptron(MLP)and random forest(RF)models for LSP are established by randomly offsetting the original landslide by 30,50,70,90 and 110 m.The LSP uncertainties are analyzed by the LSP accuracy and distribution characteristics.Finally,a semi-supervised model is proposed to relieve the LSP uncertainties.Results show that:(1)The LSP accuracies of error-based RF/MLP models decrease with the increase of landslide position errors,and are lower than those of original data-based models;(2)70 m error-based models can still reflect the overall distribution characteristics of landslide susceptibility indices,thus original landslides with certain position errors are acceptable for LSP;(3)Semi-supervised machine learning model can efficiently reduce the landslide position errors and thus improve the LSP accuracies.

Measuring Radiotherapy Setup Errors in IMRT Treated Head and Neck Cancer Patients Requiring Bilateral Neck Irradiation, NCI-Egypt Experience

Objective: We aim to quantify the magnitude of setup errors in intensity-modulated radiotherapy (IMRT) treated Head and Neck cancer patients and recommend appropriate PTV margin. Methods: 60 patients with head and neck cancer required bilateral neck irradiation were planned and treated by simultaneous integrated boost IMRT technique either treated radically or postoperative. Patients undergoing image-guided radiotherapy (IGRT) each with once weekly scheduled cone beam computed tomography (CBCT). The 3D displacements, systematic and random errors were calculated. The appropriate PTV expansion was determined using Van Herk’s formula. Results: Mean 3D displacement was 0.16 cm in the vertical direction, 0.14 cm in the horizontal direction and 0.16 cm in the longitudinal direction. Conclusion: Use of weekly CBCT allows the planning target volume (PTV) expansion to be reduced according to our setup. The appropriate clinical target volume (CTV)-PTV margin for our institute is 0.30 cm, 0.38 cm, and 0.33 cm in the horizontal, vertical, and longitudinal directions, respectively.

Prevalence of refractive errors in school-aged and preadolescent children in Colombia

AIM:To describe the distribution of refractive errors by age and sex among schoolchildren in Soacha,Colombia.METHODS:This was an observational cross-sectional study conducted in five urban public schools in the municipality of Soacha.A total of 1161 school-aged and pre-adolescent children,aged 5-12y were examined during the school year 2021-2022.Examinations included visual acuity and static refraction.Spherical equivalent(SE)was analysed as follows:myopia SE≤-0.50 D and uncorrected visual acuity of 20/25 or worse;high myopia SE≤-6.00 D;hyperopia SE≥+1.00 D(≥7y)or SE≥+2.00 D(5-6y);significant hyperopia SE≥+3.00 D.Astigmatism was defined as a cylinder in at least one eye≥1.00 D(≥7y)or≥1.75 D(5-6y).If at least one eye was ametropic,children were classified according to the refractive error found.RESULTS:Of the 1139 schoolchildren included,50.6%were male,58.8%were aged between 5 and 9y,and 12.1%were already using optical correction.The most common refractive error was astigmatism(31.1%),followed by myopia(20.8%)and hyperopia(13.1%).There was no significant relationship between refractive error and sex.There was a significant increase in astigmatism(P<0.001)and myopia(P<0.0001)with age.CONCLUSION:Astigmatism is the most common refractive error in children in an urban area of Colombia.Emmetropia decreased and myopia increased with age.

Prevalence of Refractive Errors among School Children Aged 5 to 15 Years Old at CHU-IOTA

Introduction: Undetected refractive errors constitute a health problem among school children who cannot take advantage of educational opportunities. The authors studied the prevalence of refractive errors in school children aged 5 to 15 at CHU-IOTA. Patients and Method: This is a prospective, descriptive cross-sectional study carried out in the ophthalmic-pediatrics department of CHU-IOTA, from October to November 2023. Results: We received 340 school children aged 5 to 15, among whom 111 presented ametropia, i.e. a prevalence of 32.65%. The average age was 11.42 ± 2.75 years and a sex ratio of 0.59. The average visual acuity was 4/10 (range 1/10 and 10/10). We found refractive defects: astigmatism 73.87%, hyperopia 23.87% of cases and myopia 2.25%. The decline in distance visual acuity was the most common functional sign. Ocular abnormalities associated with ametropia were dominated by allergic conjunctivitis (26.13%) and papillary excavation (6.31%) in astigmatics;allergic conjunctivitis (9.01%) and papillary excavation (7.20%) in hyperopic patients;turbid vitreous (0.90%), myopic choroidosis (0.45%) and allergic conjunctivitis (0.45%) in myopes. Conclusion: Refractive errors constitute a reality and a major public health problem among school children.

An Insight Survey on Sensor Errors and Fault Detection Techniques in Smart Spaces

The widespread adoption of the Internet of Things (IoT) has transformed various sectors globally, making themmore intelligent and connected. However, this advancement comes with challenges related to the effectiveness ofIoT devices. These devices, present in offices, homes, industries, and more, need constant monitoring to ensuretheir proper functionality. The success of smart systems relies on their seamless operation and ability to handlefaults. Sensors, crucial components of these systems, gather data and contribute to their functionality. Therefore,sensor faults can compromise the system’s reliability and undermine the trustworthiness of smart environments.To address these concerns, various techniques and algorithms can be employed to enhance the performance ofIoT devices through effective fault detection. This paper conducted a thorough review of the existing literature andconducted a detailed analysis.This analysis effectively links sensor errors with a prominent fault detection techniquecapable of addressing them. This study is innovative because it paves theway for future researchers to explore errorsthat have not yet been tackled by existing fault detection methods. Significant, the paper, also highlights essentialfactors for selecting and adopting fault detection techniques, as well as the characteristics of datasets and theircorresponding recommended techniques. Additionally, the paper presents amethodical overview of fault detectiontechniques employed in smart devices, including themetrics used for evaluation. Furthermore, the paper examinesthe body of academic work related to sensor faults and fault detection techniques within the domain. This reflectsthe growing inclination and scholarly attention of researchers and academicians toward strategies for fault detectionwithin the realm of the Internet of Things.

Relationships between Terrain Features and Forecasting Errors of Surface Wind Speeds in a Mesoscale Numerical Weather Prediction Model

Numerical weather prediction(NWP)models have always presented large forecasting errors of surface wind speeds over regions with complex terrain.In this study,surface wind forecasts from an operational NWP model,the SMS-WARR(Shanghai Meteorological Service-WRF ADAS Rapid Refresh System),are analyzed to quantitatively reveal the relationships between the forecasted surface wind speed errors and terrain features,with the intent of providing clues to better apply the NWP model to complex terrain regions.The terrain features are described by three parameters:the standard deviation of the model grid-scale orography,terrain height error of the model,and slope angle.The results show that the forecast bias has a unimodal distribution with a change in the standard deviation of orography.The minimum ME(the mean value of bias)is 1.2 m s^(-1) when the standard deviation is between 60 and 70 m.A positive correlation exists between bias and terrain height error,with the ME increasing by 10%−30%for every 200 m increase in terrain height error.The ME decreases by 65.6%when slope angle increases from(0.5°−1.5°)to larger than 3.5°for uphill winds but increases by 35.4%when the absolute value of slope angle increases from(0.5°−1.5°)to(2.5°−3.5°)for downhill winds.Several sensitivity experiments are carried out with a model output statistical(MOS)calibration model for surface wind speeds and ME(RMSE)has been reduced by 90%(30%)by introducing terrain parameters,demonstrating the value of this study.

Prevalence and Factors Associated with Refractive Errors among University Students at Mbarara University of Science and Technology, Uganda

Introduction: WHO estimated that uncorrected refractive errors are the leading cause of visual impairment and second leading cause of blindness globally. University students are prone to developing refractive errors due to their curriculum that requires a lot of near work affecting their performance and quality of life unknowingly. Genetic and environmental factors are thought to play a role in the development of refractive errors. This study addresses the paucity of knowledge about refractive errors among university students in East Africa, providing a foundation for further research. Objectives: To determine the prevalence and factors associated with refractive errors among students in the Faculty of Medicine at Mbarara University of Science and Technology. Methodology: This was a cross-sectional descriptive and analytical study in which 368 undergraduate students selected using random sampling were assessed for refractive errors from March 2021-July 2021. Eligible participants were recruited and their VA assessment done after answering a questionnaire. Students whose VA improved on pin hole had subjective retinoscopy and results were compiled and imported to STATA 14 for analysis. Results: The prevalence of refractive errors was 26.36% with (95% CI) among university students especially myopia. Myopia is most predominant at 60%, followed by 37% Astigmatism and hyperopia of 3% among medical students. Astigmatism consisted of largely myopic astigmatism 72% (26) and 28% (10) compound/mixed astigmatism only. Student positive family history of refractive error was found to have a statistically significant relationship with refractive errors with AOR 1.68 (1.04 - 2.72) (95% CI) and P (0.032). Conclusion: The prevalence of refractive errors among university students, especially myopia, was found to be high and family history was associated with students having refractive errors.

Relative peripheral refractive errors in Chinese children with myopic anisometropia

AIM:To compare relative peripheral refractive errors(RPREs)in Chinese children with and without myopic anisometropia(MAI)and to explore the relationship between RPRE and myopia.METHODS:This observational cross-sectional study included 160 children divided into two groups according to the interocular spherical equivalent refraction(SER)difference≥1.0 D in the MAI group(n=80)and<1.0 D in the non-MAI group(n=80).The MAI group was further divided into two subgroups:ΔSER<2.0 D group and ΔSER≥2.0 D group.Basic ocular biometric parameters of axial length(AL),average keratometry(Ave K),cylinder(CYL),surface regularity index(SRI),and surface asymmetry index(SAI)were recorded.In addition,multispectral refraction topography was performed to measure RPRE,and the parameters were recorded as total refraction difference value(TRDV),refraction difference value(RDV)0-10,RDV10-20,RDV20-30,RDV30-40,RDV40-53,RDV-superior(RDV-S),RDV-inferior(RDV-I),RDV-temporal(RDV-T)and RDV-nasal(RDV-N).RESULTS:In the non-MAI group,the interocular differences of all parameters of RPRE were not significant.In the MAI group,the interocular differences of TRDV,RDV10-53,RDV-S,RDV-I,RDV-T,and RDV-N were significant.In subgroup analysis,the interocular differences of TRDV,RDV30-53,RDV-I,and RDV-T were significant in ΔSER<2.0 D group and ΔSER≥2.0 D group,but the interocular differences of RDV10-30,RDV-S and RDV-N were only significant in the ΔSER≥2.0 D group.In correlation analysis,ΔTRDV,ΔRDV 10-53,ΔRDV-S,and ΔRDV-N were negatively correlated with ΔSER but positively correlated with ΔAL.CONCLUSION:The more myopic eyes have larger hyperopic RPRE in Chinese children with MAI in certain retinal range,and partialΔRPRE is closely associated with ΔSER and ΔAL.

Uncorrected refractive errors are important causes of avoidable visual impairment in Hungary: re-evaluation of two existing national data sets

·AIM: To review existing data for the prevalence of corrected, uncorrected, and inadequately corrected refractive errors and spectacle wear in Hungary.·METHODS: Data from two nationwide cross-sectional studies were analysed. The Rapid Assessment of Avoidable Blindness study collected population-based representative national data on the prevalence of visual impairment due to uncorrected refractive errors and spectacle coverage in 3523 people aged ≥50y(Group I). The Comprehensive Health Test Program of Hungary provided data on the use of spectacles in 80 290 people aged ≥18y(Group Ⅱ).·RESULTS: In Group I, almost half of the survey population showed refractive errors for distant vision, about 10% of which were uncorrected(3.2% of all male participants and 5.0% of females). The distance spectacle coverage was 90.7%(91.9% in males;90.2% in females). The proportion of inadequate distance spectacles was found to be 33.1%. Uncorrected presbyopia was found in 15.7% of participants. In all age groups(Group Ⅱ), 65.4% of females and 56.0% of males used distance spectacles,and approximately 28.9% of these spectacles were found to be inappropriate for dioptric power(with 0.5 dioptres or more). The prevalence of inaccurate distance spectacles was significantly higher in older age groups(71y and above) in both sexes.·CONCLUSION: According to this population-based data, uncorrected refractive errors are not rare in Hungary. Despite recent national initiatives, fur ther steps are required to reduce uncorrected refractive errors and associated negative effects on vision, such as avoidable visual impairment.

Psychosomatic symptoms affect radiotherapy setup errors in early breast cancer patients

Objective: To examine the trajectory of psychosomatic symptoms and to explore the impact of psychosomatic symptoms on setup error in patients undergoing breast cancer radiotherapy.Methods: A total of 102 patients with early breast cancer who received initial radiotherapy were consecutively recruited. The M.D. Anderson Symptom Inventory(MDASI) and three different anxiety scales, i.e., the Self-Rating Anxiety Scale(SAS), State-Trait Anxiety Inventory(STAI), and Anxiety Sensitivity Index(ASI), were used in this study. The radiotherapy setup errors were measured in millimetres by comparing the real-time isocratic verification film during radiotherapy with the digitally reconstructed radiograph(DRR). Patients completed the assessment at three time points: before the initial radiotherapy(T1), before the middle radiotherapy(T2), and before the last radiotherapy(T3).Results: The SAS and STAI-State scores of breast cancer patients at T1 were significantly higher than those at T2 and T3(F=24.44, P<0.001;F=30.25, P<0.001). The core symptoms of MDASI were positively correlated with anxiety severity. The setup errors of patients with high SAS scores were greater than those of patients with low anxiety levels at T1(Z=-2.01, P=0.044). We also found that higher SAS scores were associated with a higher risk of radiotherapy setup errors at T1(B=0.458, P<0.05).Conclusions: This study seeks to identify treatment-related psychosomatic symptoms and mitigate their impact on patients and treatment. Patients with early breast cancer experienced the highest level of anxiety before the initial radiotherapy, and then, anxiety levels declined. Patients with high somatic symptoms of anxiety may have a higher risk of radiotherapy setup errors.

PENALIZED LEAST SQUARE IN SPARSE SETTING WITH CONVEX PENALTY AND NON GAUSSIAN ERRORS

This paper consider the penalized least squares estimators with convex penalties or regularization norms.We provide sparsity oracle inequalities for the prediction error for a general convex penalty and for the particular cases of Lasso and Group Lasso estimators in a regression setting.The main contribution is that our oracle inequalities are established for the more general case where the observations noise is issued from probability measures that satisfy a weak spectral gap(or Poincaré)inequality instead of Gaussian distributions.We illustrate our results on a heavy tailed example and a sub Gaussian one;we especially give the explicit bounds of the oracle inequalities for these two special examples.

Numerical Investigations on the Resonance Errors of Multiscale Discontinuous Galerkin Methods for One-Dimensional Stationary Schrödinger Equation

In this paper,numerical experiments are carried out to investigate the impact of penalty parameters in the numerical traces on the resonance errors of high-order multiscale discontinuous Galerkin(DG)methods(Dong et al.in J Sci Comput 66:321–345,2016;Dong and Wang in J Comput Appl Math 380:1–11,2020)for a one-dimensional stationary Schrödinger equation.Previous work showed that penalty parameters were required to be positive in error analysis,but the methods with zero penalty parameters worked fine in numerical simulations on coarse meshes.In this work,by performing extensive numerical experiments,we discover that zero penalty parameters lead to resonance errors in the multiscale DG methods,and taking positive penalty parameters can effectively reduce resonance errors and make the matrix in the global linear system have better condition numbers.

Application of Variance Component Analysis (ANOVA) in Setup Errors and PTV Margins for Lung Cancer with Stereotactic Body Radiation Therapy (SBRT)

Purpose: To investigate the feasibility of applying ANOVA newly proposed by Yukinori to verify the setup errors, PTV (Planning Target Volume) margins, DVH for lung cancer with SBRT. Methods: 20 patients receiving SBRT to 50 Gy in 5 fractions with a Varian iX linear acceleration were selected. Each patient was scanned with kV-CBCT before the daily treatment to verify the setup position. Two other error calculation methods raised by Van Herk and Remeijer were also compared to discover the statistical difference in systematic errors (Σ), random errors (σ), PTV margins and DVH. Results: Utilizing two PTV margin calculation formulas (Stroom, Van Herk), PTV calculated by Yukinori method in three directions were (5.89 and 3.95), (5.54 and 3.55), (3.24 and 0.78) mm;Van Herk method were (6.10 and 4.25), (5.73 and 3.83), (3.51 and 1.13) mm;Remeijer method were (6.39 and 4.57), (5.98 and 4.10), (3.69 and 1.33) mm. The volumes of PTV using Yukinori method were significantly smaller (P < 0.05) than Van Herk method and Remeijer method. However, dosimetric indices of PTV (D98, D50, D2) and for OARs (Mean Dose, V20, V5) had no significant difference (P > 0.05) among three methods. Conclusions: In lung SBRT treatment, due to fraction reduction and high level of dose per fraction, ANOVA was able to offset the effect of random factors in systematic errors, reducing the PTV margins and volumes. However, no distinct dose distribution improvement was founded in target volume and organs at risk.

An Evaluation of Inter-Fractional Set-Up Errors in Patients Treated with Distinct Immobilization Equipment for Varying Anatomical Regions

This study aims to evaluate inter-fractional set-up errors in patients treated with distinct immobilization equipment (thermoplastic mask, knee-fix and feet-fix, wing board and vac-lok) for four anatomical regions including brain, head and neck (HN), thorax and pelvis. Data of randomly selected 140 patients who were treated for four anatomical regions were obtained using Hi-Art Helical Tomotherapy (HT) system. Pre-treatment planning was based on automatic registration readings of computed tomography (CT) and mega-voltage computed tomography (MVCT) on a daily basis. Distinct immobilization equipment was used for varying anatomical regions. Individual mean set-up error (M), systematic error (Σ), and random error (σ) values were calculated through daily translational and rotational deviation values. The size of translational, systematic and random error was 1.31 - 4.93 mm for brain, 2.28 - 4.88 mm for HN, 4.04 - 9.90 mm for thorax, and 6.34 - 14.68 mm for pelvis. Rotational values were as follows: 0.06&deg - 0.73&deg for brain, 0.42&deg - 0.6&deg for HN, 0.48&deg - 1.14&deg for thorax and 0.65&deg - 1.05&deg for pelvis. The highest translational, systematic and random error value was obtained from the pelvic regional. The highest standard and random error value in pitch and roll was produced in the rotational direction of the pelvis (0.05° and 0.71°), while the highest error value in yaw was (1.14°) produced from thorax. Inter-fractional set-up errors were most commonly produced in the pelvis, followed by thorax. Our study results suggest that the highest systematic and random errors are found for thorax and pelvis. Distinct immobilization equipment was important in these results. Safety margins around the clinical target volume (CTV) are changeable for different anatomical regions. A future work could be developed to new equipment for immobilization because of the reduced margins CTV.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces

A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.