Non-homogeneous Data Research Articles

Multidimensional Comparative Analysis of Bioactive Phenolic Compounds of Honeys of Various Origin.

Honey is a natural product which owes its health benefits to its numerous bioactive compounds. The composition of honey is highly diverse and depends on the type of honey and its origin. Antioxidant capacity arises mainly from the total content of polyphenols and their composition. The aim of this study was to perform a multidimensional comparative analysis of phenolic compounds of honeys of various origins. Honeydew, buckwheat, manuka, Malaysian and goldenrod honeys had the highest antioxidant capacity (above 400 mg Trolox equivalents kg−1). These honeys were also characterized by the highest total polyphenol content (about 2500 mg gallic acid equivalents (GAE) kg−1) and the highest total flavonoid content (1400–1800 mg catechin equivalents (CAE) kg−1). Other honeys had much lower antioxidant properties. A multidimensional analysis of the profiles of phenolic compounds showed that honeys constitute a non-homogeneous data set and manuka honey was in contrast to other samples. Principal component analysis (PCA) (based on 18 phenolic compounds) distinguished honeys into five groups. Manuka, Malaysian and honeydew honeys created their own separate groups and the location of other honeys was variable. Ultra-high-performance liquid chromatography (UHPLC) analysis demonstrated that profiles of polyphenols in honeys were highly varied. Caffeic acid, datiscetin and rhamnetin were characteristic compounds for manuka honey. Quercetin, kaempferol and apigenin were present in all honeys except Malaysian honey. The antioxidant properties and the profiles of bioactive phenolic compounds of honeys were miscellaneous. The richest sources of polyphenols were local buckwheat and honeydew honeys, alongside exotic manuka and Malaysian honeys. These honeys could provide valuable ingredients to the human diet, helping to prevent diseases.

An Information Elasticity Framework for the Adaptive Matched Filter

The adaptive matched filter (AMF) uses a number of training samples observed by the radar to estimate the unknown disturbance covariance matrix of a cell under test. In general, as the number of homogeneous training samples increases, the detection performance of the AMF improves up to a theoretical limit (defined by the performance of a matched filter detector where the disturbance covariance is known). However, radar data are nonhomogeneous in practice. Consequently, a high number of training samples is typically undesirable, since nonhomogeneous training data cause detection performance to suffer. Thus, a decision maker (DM) must consider these tradeoffs when selecting this number of training samples, along with other decision parameters for the AMF. Using the concept of information elasticity, this tradeoff behavior is characterized for decisions that are relevant to a DM. A simple user defined constraint function is proposed, characterizing the relative cost of selecting different decisions. Using a multi-objective optimization (MOO) technique known as compromise programming, information overload is observed, in that increasing the cost of decisions improves performance up to a point, beyond which increasing the cost no longer provides meaningful benefit. Using this framework, a cost-efficient solution is selected.

The Acute Effects of Dynamic and Static Stretching on Tennis Serve Targeting Performance

The study investigates the acute effects of dynamic and static stretching on the tennis serve targeting performance of amateur tennis players. Twenty male athletes who were between the ages of 16-24 years and played tennis for at least 1 year (21.40±2.16 years, 181±0.06 cm, 71.85±7.42 kg, tennis playing time 1.55±0.88 years) voluntarily participated in the study. Prior to the pre-tests and after applying the traditional warm-up protocol, serve targeting test (STT) was applied to all participants. In the post-tests, STT was used after applying three different warm-up methods on three different days (48-hour rest interval). The warm-up stages included No Treatment (NT) (jogging, rally), Static Stretching (SS) and Dynamic Stretching (DS). In the statistical analysis, the homogeneity of the data was investigated using the Shapiro Wilk test. The Wilcoxon test was used to compare the pre-test and post-test results of the non-homogeneous data; Friedman test was used to compare the three different stretching methods with each other; in the paired comparisons of the groups, the paired samples t-test was used for the homogenous data and Wilcoxon test was used for the non-homogeneous data. In conclusion, stretching exercises before serving increased the serve targeting performance and the increase in the dynamic stretching exercises was higher than that in static stretching exercises.

Microarray Image Analysis: From Image Processing Methods to Gene Expression Levels Estimation

Microarray image processing leads to the characterization of gene expression levels simultaneously, for all cellular transcripts (mRNAs) in a single experiment. The calculation of expression levels for each microarray spot/gene is a crucial step to extract valuable information. By measuring the mRNA levels for the whole genome, the microarray experiments are capable to study functionality, pathological phenotype, and response of cells to a pharmaceutical treatment. The processing of the extensive number of non-homogeneous data contained in microarray images is still a challenge. We propose a density based spatial clustering procedure driven by a level-set approach for microarray spot segmentation together with a complete set of quality measures used to evaluate the proposed method compared with existing approaches for gene expression levels estimation. The set of quality measures used for evaluation include: regression ratios, intensity ratios, mean absolute error, coefficient of variation and fold change factor. We applied the proposed image processing pipeline to a set of microarray images and compared our results with the ones delivered by Genepix, using the aforementioned quality measures. The advantage of our proposed method is highlighted by a selection of up-regulated genes that had been identified exclusively by our approach. These genes prove to add valuable information regarding the biological mechanism activated as a response of Arabidopsis T to pathogen infection.

OCCLUDED AREA REMOVING FROM HANDHELD LASER SCANNER DATA DURING 3D BUILDING MODELLING

Abstract. 3D building modelling has been turned to be one of the most interesting and hottest subjects in photogrammetry in last two decades, and it seems that photogrammetry provides the only economic means to acquire truly 3D city-data. Most of the researches proposed methods for 3d building modelling in LoD2 using aerial images and LIDAR data and the produced models will be enriched by oblique images, therefore there is always a demand for a user to interpret the façade or in other manual building reconstruction process the operator should draw boundaries to represent the building model and the process will be too time-consuming for 3d modelling for a whole city. Creating building facade models for a whole city requires considerable work, therefore for decades, much research has been dedicated to the automation of this reconstruction process. Nowadays researchers attempt to recommend a new method which is flexible to model hug variety of buildings and has a solution for several challenges such as irrelevant objects (pedestrians, trees, traffic signs, etc.), occluded areas and non-homogenous data. Based on various 3d building models applications, namely navigation systems, location-based system, city planning and etc. the demand for adding semantic features (such as windows and doors) is increasing and becoming more essential, therefore simple blocks as the representation of 3d buildings aren’t sufficient anymore. Therefore 2.5 models which show the façade details using pixel values have been substituted by LoD3 models recently.The lack of automation in image based approaches can be explained by the difficulties in image interpretation. Specifically, factors like illumination and occlusion can cause considerable confusion for machine understanding and some conditions (relative orientation, feature matching, etc.) need to be accurately determined to transfer image pixels to 3D coordinates. In recent years, terrestrial laser scanning data has been proven as a valuable source for building facade reconstruction. The point density of stationary laser scanning in urban areas can be up to hundreds or thousands of points per square meter, which is high enough for documenting most details on building facades. In comparison with image-based modelling, several steps such as image matching, intersection and resection will be eliminated, while there is no need to image interpret in laser data-based reconstruction approaches, these methods face major challenges such as extracting meaningful structures from a huge amount of data.This paper presents a data-driven algorithm for façade reconstruction, using a handheld laser scanner, Zebedee. The mentioned device is consisting of 2d laser scanner and an inertial measurement unit mounted on one or two springs, it has 270-degree field of view. Its mass is 210 g which makes it ideal for low measurement and it is maximum range is 30 m. The proposed method was implemented by using the Zebedee point cloud in order to determine the challenges of zeb1 data and ensure that the introduced device can be practical for 3d reconstruction.Due to obstacle existence, operator gross errors while data capturing and façade elements arrangement, there will always be occluded area and shadows in produced data. Occluded area cause tribulation in machine understanding and problems for automatic reconstruction algorithms. The proposed method represents a new way to detect occluded area and remove the artificial objects which are produced by them. The 3d point cloud is used to cover all façade elements and details, also image matching and producing 3-dimensional data steps will be omitted from the process.The proposed workflow is indicated in figure 1. Most researches such as road, building or other objects detection and reconstruction put ground points detection in priority in order to decrease data volume and processing time, so as a pre-processing step, point cloud is classified into two separate groups (non-ground and ground points).

Coarse-to-Fine UAV Target Tracking With Deep Reinforcement Learning

The aspect ratio of a target changes frequently during an unmanned aerial vehicle (UAV) tracking task, which makes the aerial tracking very challenging. Traditional trackers struggle from such a problem as they mainly focus on the scale variation issue by maintaining a certain aspect ratio. In this paper, we propose a coarse-to-fine deep scheme to address the aspect ratio variation in UAV tracking. The coarse-tracker first produces an initial estimate for the target object, then a sequence of actions are learned to fine-tune the four boundaries of the bounding box. The coarse-tracker and the fine-tracker are designed to have different action spaces and operating target. The former dominates the entire bounding box and the latter focuses on the refinement of each boundary. They are trained jointly by sharing the perception network with an end-to-end reinforcement learning architecture. Experimental results on benchmark aerial data set prove that the proposed approach outperforms existing trackers and produces significant accuracy gains in dealing with the aspect ratio variation in UAV tracking. Note to Practitioners —During the past years, unmanned aerial vehicle (UAV) have gained much attention for both industrial and consumer uses. It is in urgent demand to endow the UAV with intelligent vision-based techniques, and the automatic target following via visual tracking methods as one of the most fundamental intelligent features could promote various applications of UAVs, such as surveillance, augmented reality, and behavior modeling. Nonetheless, the primary issue of a UAV-based tracking method is the platform itself: it is not stable, it tends to have sudden movements, it generates nonhomogeneous data (scale, angle, rotation, depth, and so on), all of them tend to change the aspect ratio of the target frequently and further increase the difficulty of object tracking. This paper aims to address the aspect ratio change (ARC) problem in UAV tracking. We present a coarse-to-fine strategy for UAV tracking. Specifically, the coarse bounding box is obtained to locate the target firstly. Then, a refinement scheme is performed on each boundary to further improve the position estimate. The tracker is proved to be effective to increase the resistance to the ARC. Such a method can be implemented on UAV to improve the target-following performance.

ANALISIS STRUCTURAL EQUATION MODELING (SEM) DENGAN MULTIPLE GROUP MENGGUNAKAN R

Structural Equation Model (SEM) is a statistical technique with simultaneous processing involves measurement errors, indicator variables, and latent variables. SEM is used to test hypotheses that state the relationships between latent variables when latent variables have been assessed through each of the indicator variables. Multiple Group SEM is a basic model analysis that uses more than one sample. This analysis aims to determine whether the components or models of measurement and structural models are invariant for the two sample groups. In this study, the data generated by some requirements. First, the data generated with sample size n = 250. The first generated data is homogeneous data where the measurement model is the same as the structural model in group 1 and group 2, while the second data is non-homogeneous data where the measurement model and the structural model in group 1 and group 2 is not the same. The data was analyzed using the help of the lavaan package available in R to obtain SEM estimation results and Goodness of Fit Model from some data that was formed. From the results of the merger of the two groups, it shows that the invariant of the two models with the largest df (63) which is Fit Mean model states the simplest model. However, the smallest df (48) with Fit.configural model states the most complex model.
 Keywords: SEM, Multiple Group, R Program

On Novel Nonhomogeneous Multivariable Grey Forecasting Model NHMGM

A novel nonhomogeneous multivariable grey forecasting model termed NHMGM(1,m,kp,c) is proposed in this paper for use in nonhomogeneous multivariable exponential data sequences. The NHMGM(1,m,kp,c) model is able to reflect the nonlinear relation of the data sequences in the system, and it is proved that many classic grey forecasting models can be derived from NHMGM(1,m,kp,c) model. Parameters of the novel model are obtained by using least square method, and the time response function is given. A numerical example is presented to show the effectiveness of the proposed model, six different grey forecasting models are built for modeling, and two popular accuracy criteria (ARPE and MAPE) are adopted to test the reliability of the novel model. The example demonstrates that NHMGM-2 model provides favorable performance compared with the other five grey models. Additionally, the multiplication transformation properties of NHMGM(1,m,kp,c) are systematically analysed, which establish a theoretical foundation for further applications of the model.

The Acute Effects of Dynamic and Static Stretching on Tennis Serve Targeting Performance

The study investigates the acute effects of dynamic and static stretching on the tennis serve targeting performance of amateur tennis players. Twenty male athletes who were between the ages of 16-24 years and played tennis for at least 1 year (21.40±2.16 years, 181±0.06 cm, 71.85±7.42 kg, tennis playing time 1.55±0.88 years) voluntarily participated in the study.Prior to the pre-tests and after applying the traditional warm-up protocol, serve targeting test (STT) was applied to all participants. In the post-tests, STT was used after applying three different warm-up methods on three different days (48-hour rest interval). The warm-up stages included No Treatment (NT) (jogging, rally), Static Stretching (SS) and Dynamic Stretching (DS).In the statistical analysis, the homogeneity of the data was investigated using the Shapiro Wilk test. The Wilcoxon test was used to compare the pre-test and post-test results of the non-homogeneous data; Friedman test was used to compare the three different stretching methods with each other; in the paired comparisons of the groups, the paired samples t-test was used for the homogenous data and Wilcoxon test was used for the non-homogeneous data. In conclusion, stretching exercises before serving increased the serve targeting performance and the increase in the dynamic stretching exercises was higher than that in static stretching exercises.

Power and level robustness of a test for composite hypotheses under independent non-homogeneous data

We consider a class of density power divergence based tests for composite hypotheses under non-homogeneous data. This note provides a rigorous derivation of the power and level influence functions to theoretically justify their robustness with applications to fixed-carrier linear regressions.

Towards stroke prediction using electronic health records

BackgroundAs of 2014, stroke is the fourth leading cause of death in Japan. Predicting a future diagnosis of stroke would better enable proactive forms of healthcare measures to be taken. We aim to predict a diagnosis of stroke within one year of the patient’s last set of exam results or medical diagnoses.MethodsAround 8000 electronic health records were provided by Tsuyama Jifukai Tsuyama Chuo Hospital in Japan. These records contained non-homogeneous temporal data which were first transformed into a form usable by an algorithm. The transformed data were used as input into several neural network architectures designed to evaluate efficacy of the supplied data and also the networks’ capability at exploiting relationships that could underlie the data. The prevalence of stroke cases resulted in imbalanced class outputs which resulted in trained neural network models being biased towards negative predictions. To address this issue, we designed and incorporated regularization terms into the standard cross-entropy loss function. These terms penalized false positive and false negative predictions. We evaluated the performance of our trained models using Receiver Operating Characteristic.ResultsThe best neural network incorporated and combined the different sources of temporal data through a dual-input topology. This network attained area under the Receiver Operating Characteristic curve of 0.669. The custom regularization terms had a positive effect on the training process when compared against the standard cross-entropy loss function.ConclusionsThe techniques we describe in this paper are viable and the developed models form part of the foundation of a national clinical decision support system.

Suture techniques during laparoscopic and robot-assisted partial nephrectomy: a systematic review and quantitative synthesis of peri-operative outcomes.

To summarize the available evidence on renorrhaphy techniques and to assess their impact on peri-operative outcomes after minimally invasive partial nephrectomy (MIPN). A systematic review of the literature was performed in January 2018 without time restrictions, using MEDLINE, Cochrane and Web of Science databases according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses statement recommendations. Studies providing sufficient details on renorrhaphy techniques during laparoscopic or robot-assisted partial nephrectomy and comparative studies focused on peri-operative outcomes were included in qualitative and quantitative analyses, respectively. Overall, 67 and 19 studies were included in the qualitative and quantitative analyses, respectively. The overall quality of evidence was low. Specific tumour features (i.e. size, hilar location, anatomical complexity, nearness to renal sinus and/or urinary collecting system), surgeon's experience, robot-assisted technology, as well as the aim of reducing warm ischaemia time and the amount of devascularized renal parenchyma preserved represented the key factors driving the evolution of the renorrhaphy techniques during MIPN over the past decade. Quantitative synthesis showed that running suture was associated with shorter operating and ischaemia time, and lower postoperative complication and transfusion rates than interrupted suture. Barbed suture had lower operating and ischaemia time and less blood loss than non-barbed suture. The single-layer suture technique was associated with shorter operating and ischaemia time than the double-layer technique. No comparisons were possible concerning renal functional outcomes because of non-homogeneous data reporting. Renorrhaphy techniques significantly evolved over the years, improving outcomes. Running suture, particularly using barbed wires, shortened the operating and ischaemia times. A further advantage could derive from avoiding a double-layer suture.

Initial-boundary value problem of the Navier–Stokes equations in the half space with nonhomogeneous data

This paper discusses the solvability (global in time) of the initial-boundary value problem of the Navier-stokes equations in the half space when the initial data $ h\in \dot{ B}_{q \sigma}^{\alpha-\frac{2}{q}}(\R_+)$ and the boundary data $ g\in \dot{ B}_q^{\alpha-\frac{1}{q},\frac{\al}{2}-\frac{1}{2q}}({\mathbb R}^{n-1}\times {\mathbb R}_+) $ with $g_n\in \dot B^{\frac12 \alpha}_q ({\mathbb R}_+; \dot B^{-\frac1q}_q ({\mathbb R}^{n-1}))\cap L^q({\mathbb R}_+;\dot{B}^{\alpha-\frac{1}{q}}(\Rn))$, for any $0<\alpha<2$ and $q =\frac{n+2}{\alpha+1}$. Compatibility condition is required for $h$ and $g$.

A Nonhomogeneous Multivariable Grey Prediction NMGM Modeling Mechanism and Its Application

The purpose of this paper is to explore modeling mechanism of a nonhomogeneous multivariable grey prediction NMGM(1, m, kα) model and its application. Although multi-variable grey prediction MGM(1, m) model has been employed in many fields, its prediction results are not always satisfactory. Traditional MGM(1, m) model is constructed on the hypothesis that original data sequences are in accord with homogeneous index trend; however, the nonhomogeneous index data sequences are the most common data existing in all systems, and how to handle multivariable nonhomogeneous index data sequences is an urgent problem. This paper proposes a novel nonhomogeneous multivariable grey prediction model termed NMGM(1, m, kα) to deal with those data sequences that are not in accord with homogeneous index trend. Based on grey prediction theory, by least square method and solutions of differential equations, the modeling mechanism and time response function of the proposed model are expounded. A case study demonstrates that the novel model provides preferable prediction performance compared with traditional MGM(1, m) model. This work is an extension of the multivariable grey prediction model and enriches the study of grey prediction theory.

Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

The telegraph equation is one of the important equations of mathematical physics. In this work, a spectral collocation scheme is proposed for the numerical solutions of one- and two-dimensional linear telegraph equations and telegraph equations with nonlinear forcing term. The homogeneous initial and boundary conditions are satisfied exactly by expanding the unknown variable using polynomial bases of functions which are built upon the Jacobi polynomials. The suggested scheme is successfully developed for the aforementioned problem with nonhomogeneous data. Extensive numerical experiments are presented to verify the efficiency of the proposed scheme.

Implementation of ergonomics in the management of parking increasing the quality of living parking park in mall Robinson Denpasar city

The problems that often arise in the area of Denpasar City mostly caused by parking problems at the centers of activities such as shopping centers. The problems that occur not only because of the large number of vehicles that parked but also the result of the condition of parking officers who have not received attention, there is no concern about the physical condition of parking attendants because doing night guard duty. To improve the quality of parking officer, ergonomic parking lot is improved through the application of appropriate technology with systemic, holistic, interdisciplinary and participatory approach. The general objective of the research is to know the implementation of ergonomics in parking management on the improvement of the quality of parking officer in Robinson shopping center. The indicator of the quality of the parking officer work is the decrease of musculoskeletal complaints, fatigue, workload, boredom and increasing work motivation. The study was conducted using the same subject design, involving 10 subjects as a simple random sample. Intervention is done by arrangement of ergonomic basement motorcycle parking. Measurements done before and after repair. Washing out (WO) for 14 days. The data obtained were analyzed descriptively, tested normality (shapirowilk) and homogeneity (Levene Test). For normal and homogeneous distribution data, different test with One Way Anova, different test between Period with Post Hoc. Normally distributed and non-homogeneous data, different test with Friedman Test, different test between periods using Wilcoxon test. Data were analyzed with significance level of 5%. The results showed that the implementation of ergonomic in the management of parking area of the court decreased musculoskeletal complaints by 15.10% (p <0.05), decreased fatigue rate by 22.06% (p <0.05), decreased workload by 21, 90 % (P <0,05), decrease boredom 15,85% (p <0,05) and motivation improvement 37, 68% (p <0,05). It is concluded that the implementation of ergonomics in parking management of the parking lot improves the quality of the parking officer work from: (1) decrease of musculoskeletal complaints, (2) decrease of melting rate, (3) decrease of parking workload, decreasing boredom and increasing work motivation.

A novel animal model of hypoxic-ischemic encephalopathy established by tracheal clamping

Objective To establish a simple, reliable and reproducible animal model of neonatal hypoxic-ischemic encephalopathy (HIE) with similar clinical pathological process to neonates. Methods Seven days after birth, 180 Sprague-Dawley (SD) rats were randomly divided into six groups: blank control group, experimental control group and four hypoxia groups (8, 10, 12 and 14 min hypoxia groups). Those in the experimental groups were locally anesthetized with 5% lidocaine to separate their tracheas through blunt dissection, followed by tracheal clamping with vascular clamp for 8, 10, 12 and 14 min, respectively. Rats in the experimental control group were only treated with blunt dissection of trachea. No intervention was given to the blank control group. Due to significant reduction in rat survival rate after 14 min of hypoxia, no further morphological or behavioral examination was performed in this group. Rat brain tissue sections were stained with hematoxylin-eosin (HE) 12 h after modeling. Three days after modeling, the rat brain was weighted and the apoptosis of neural cells was detected with terminal deoxynucleotidyl transferase(TdT) mediated dUTP nick end labeling (TUNEL). Morris water maze was used to screen cognitive impairment in these rats at the age of two months. One-way analysis of variance was used for statistical analysis. SNK test and Dunnett 's T3 test were performed to compare homogeneous and non-homogeneous data between groups. Results Systemic cyanosis, loss of consciousness, paled body, urinary and fecal incontinence, twitching of the limbs and tail and other abnormal behavior were induced by hypoxia. Ischemic necrosis, bleeding, nucleus shrinkage in a large number of neurons and hyperchromatic nuclei were observed in the 8, 10 and 12 min hypoxia groups. Three days after modeling, brain weights of rats in the 8, 10 and 12 min hypoxia groups were lower than those of the blank control group and experimental control group [(1.16±0.07), (1.04±0.06), (0.97±0.12), (1.31±0.06) and (1.28±0.09) g, F=36.437, P<0.001]. However, the numbers of apoptotic cortical [(22.83±4.52), (30.25±3.02), (39.18±5.04), (7.96±2.24) and (8.86±2.49)/400 scope field, F=164.532, P<0.001] and hippocampal CA3 neurons of that three hypoxia groups were higher than those of the two control groups [(14.63±2.26), (20.25±3.02), (24.81±1.98), (4.75±2.66) and (6.67±1.78)/400 scope field, F=141.026, P<0.001]. At the age of two months, rats in the 8, 10 and 12 min hypoxia groups had longer escape latency [(17.99±6.48), (23.07±9.90), (38.94±32.46), (14.37±6.06) and (12.78±7.21) s, F=26.912, P<0.001] and fewer times of platform crossings than those in the control group and experimental control group [(5.00±1.41), (4.90±1.29), (3.75±1.83), (7.57±1.16) and (7.14±1.15) times, F=14.336, P<0.001]. Conclusions Pathological changes in brain tissues and behaviors of rats after modeling are in line with the characteristics of classic animal model of HIE and similar to the clinical pathology and physiology of HIE, and this could be a new, simple, reliable and reproducible animal model of HIE, being capable of controlling the duration of hypoxia accurately. Key words: Hypoxia-ischemia, brain; Disease models, animal; Trachea; Constriction

Homogenization in perforated domains: a Stokes grill and an adsorption process

ABSTRACTWe address the homogenization of a model for the diffusion of a substance through an incompressible fluid in a perforated domain , . The perforations (obstacles for the fluid) are periodically placed along a surface . Their size is much smaller than the period . An adsorption phenomenon can occur on the boundaries of the perforations, where we assume a nonlinear law with a large adsorption parameter. The unknowns of the problem are the velocity of the fluid and the concentration of the substance. Using matched asymptotic expansions, we obtain the homogenized models which depend on the relations between the parameters , sizes and adsorption. In particular, we extend the results in the literature for non-homogeneous data on the velocity and general shapes of perforations for the adsorption problem.

Instationary Generalized Stokes Equations in Partially Periodic Domains

We consider an instationary generalized Stokes system with nonhomogeneous divergence data under a periodic condition in only some directions. The problem is set in the whole space, the half space or in (after an identification of the periodic directions with a torus) bounded domains with sufficiently regular boundary. We show unique solvability for all times in Muckenhoupt weighted Lebesgue spaces. The divergence condition is dealt with by analyzing the associated reduced Stokes system and in particular by showing maximal regularity of the partially periodic reduced Stokes operator.

Gradient Continuity for Nonlinear Obstacle Problems

We prove that the gradients of solutions to obstacle problems are continuous if the gradients of obstacles satisfy a Dini type continuity assumption. We also consider coefficients and nonhomogeneous data and investigate their regularity conditions to obtain gradient continuity, extending to the constrained case results starting with those presented by Mingione (J Eur Math Soc 13:459–486, 2011).