C^(1,α)-PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS

We prove C1.α-partial regularity of weak solutions of nonlinear elliptic systems under the main assumption that Aia and Bi satisfy the controllable growth condition or the natural growth condition.

From the new Austrian tunneling method to the geoengineering condition evaluation and dynamic controlling method

The new Austrian tunneling method （NATM） is widely applied in design and construction of underground engineering projects. When the type and distribution of unfavorable geological bodies （UGBs） associated with their influences on geoengineering are complicated or unfortunately are overlooked, we should pay more attentions to internal features of rocks grades IV and V （even in local but mostly controlling zones）. With increasing attentions to the characteristics, mechanism and influences of engineering construction-triggered geohazards, it is crucial to fully understand the disturbance of these geohazards on project construction. A reasonable determination method in construction procedure, i.e. the shape of working face, the type of engineering support and the choice of feasible procedure, should be considered in order to mitigate the construction-triggered geohazards. Due to their high sensitivity to groundwater and in-situ stress, various UGBs exhibit hysteretic nature and failure modes. To give a complete understanding on the internal causes, the emphasis on advanced comprehensive geological forecasting and overall reinforcement treatment is therefore of more practical significance. Compre- hensive evaluation of influential factors, identification of UGB, and measures of discontinuity dynamic controlling comprises the geoengineering condition evaluation and dynamic controlling method. In a case of a cut slope, the variations of UGBs and the impacts of key environmental factors are presented, where more severe construction-triggered geohazards emerged in construction stage than those predicted in design and field investigation stages. As a result, the weight ratios of different influential factors with respect to field investigation, design and construction are obtained.

PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.

Chemo-selective couplings of anilines and acroleins/enones under substrate control and condition control

Rh(III)‐catalyzed C–H activation of N‐protected anilines and chemo‐divergent couplings with acroleins/enones have been realized for synthesis of three classes of heterocycles.The oxidative coupling of N‐pyridylaniline afforded dihydroquinolones with the acrolein being a major hydrogen acceptor.When the directing group was replaced by pyrimidyl in the same system,redox‐neutral coupling occurred to afford hemiaminal ethers.Oxidative annulation of N‐pyridylanilines with enones using AgBF4 oxidant afforded atropisomeric quinolinium salts.

Describing failure in geomaterials using second-order work approach

Geomaterials are known to be non-associated materials. Granular soils therefore exhibit a variety of failure modes, with diffuse or localized kinematical patterns. In fact, the notion of failure itself can be confusing with regard to granular soils, because it is not associated with an obvious phenomenology. In this study, we built a proper framework, using the second-order work theory, to describe some failure modes in geomaterials based on energy conservation. The occurrence of failure is defined by an abrupt increase in kinetic energy. The increase in kinetic energy from an equilibrium state, under incremental loading, is shown to be equal to the difference between the external second-order work,involving the external loading parameters, and the internal second-order work, involving the constitutive properties of the material. When a stress limit state is reached, a certain stress component passes through a maximum value and then may decrease. Under such a condition, if a certain additional external loading is applied, the system fails, sharply increasing the strain rate. The internal stress is no longer able to balance the external stress, leading to a dynamic response of the specimen. As an illustration, the theoretical framework was applied to the well-known undrained triaxial test for loose soils. The influence of the loading control mode was clearly highlighted. It is shown that the plastic limit theory appears to be a particular case of this more general second-order work theory. When the plastic limit condition is met, the internal second-order work is nil. A class of incremental external loadings causes the kinetic energy to increase dramatically, leading to the sudden collapse of the specimen, as observed in laboratory.

Dynamic Control of Defective Gap Mode Through Defect Location

A one dimensional model is developed for defective gap mode（DGM）with two types of boundary conditions：conducting mesh and conducting sleeve.For a periodically modulated system without defect,the normalized width of spectral gaps equals to the modulation factor,which is consistent with previous studies.For a periodic system with local defects introduced by the boundary conditions,it shows that the conducting-mesh-induced DGM is always well confined by spectral gaps while the conducting-sleeve-induced DGM is not.The defect location can be a useful tool to dynamically control the frequency and spatial periodicity of DGM inside spectral gaps.This controllability can be potentially applied to the interaction between gap eigenmodes and energetic particles in fusion plasmas,and optical microcavities and waveguides in photonic crystals.

Effects of two types of exercise training on psychological well-being,sleep,quality of life and physical fitness in patients with high-grade glioma(WHO III and IV):study protocol for a randomized controlled trial

Background:There is existing evidence on whether and to what degree regular exercise training improves the quality of life(QoL)among cancer survivors.However,in regards to patients with high-grade glioma(HGG;WHO grade III and IV),no conclusive study has been performed so far.The present trial aims to fill this gap by examining whether psychological well-being,sleep,QoL and physical fitness might be improved with two different types of exercise,as compared to an active control condition.Active control condition represent individuals participating at regular meetings to talk about their current life situation,though,the meetings were not intended as that of the psychotherapy group.Regular meetings are of the same frequency,duration,and intensity as the exercise interventions.Methods:A total of 45 patients with HGG after undergoing neurosurgery and adjuvant radiotherapy,chemotherapy,or chemoradiotherapy will be consecutively and randomly assigned to(a)an endurance training,(b)a resistance training or(c)to an active control condition.The intervention will last for 6 consecutive weeks,consisting of 2 weekly sessions(30-45 min per session).Measurements would take place at three time points,namely at the beginning of the study(baseline),3 weeks after the beginning of the study,and 6 weeks after the beginning of the study.The last measurement also represents the end of the study.Aerobic exercise performance will be assessed objectively with a 6-min walking test,and a handgrip test will be used to assess the upper body strength.Further,participants will complete a battery of questionnaires covering sociodemographic information,QoL,sleep quality and sleep patterns,coping with stress,state-and trait-anxiety,depression,and fatigue.In parallel,experts will use the Hamilton Depres-sion Rating Scale to determine and rate participants’symptoms of depression.Significance:The present study will be the first to investigate and compare the impact of two different exercise modalities,namely endurance and resistance training,on physical fitness and dimensions of well-being,and sleep among patients with HGG who underwent neurosurgery followed by adjuvant radiotherapy,chemotherapy,or chemoradiotherapy.Importantly,unlike the majority of previous studies,the control condition consists of an active set-up to detect possible factual beneficial effects of exercise training,irrespective of social interactions.

The method of p-harmonic approximation and optimal interior partial regularity for energy minimizing p-harmonic maps under the controllable growth condition

In this paper, we are concerned with the partial regularity for the weak solutions of energy minimizing p-harmonic maps under the controllable growth condition. We get the interior partial regularity by the p-harmonic approximation method together with the technique used to get the decay estimation on some Degenerate elliptic equations and the obstacle problem by Tan and Yan. In particular, we directly get the optimal regularity.

Uncoupled PID Control of Coupled Multi-Agent Nonlinear Uncertain Systems

In this paper, PID（proportional-integral-derivative） controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.

PARTIAL REGULARITY RESULT OF SUPERQUADRATIC ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of A-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal H¨older exponent for the derivative of the weak solutions on the regular set.