AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.

Stochastic analysis of load-transfer mechanism of energy piles by random finite difference model

The surge in demand for renewable energy to combat the ever-escalating climate crisis promotes development of the energy-saving,carbon saving and reduction technologies.Shallow ground-source heat pump(GSHP)system is a promising carbon reduction technology that can stably and effectively exploit subsurface geothermal energy by taking advantage of load-bearing structural elements as heat transfer medium.However,the transformation of conventional geo-structures(e.g.piles)into heat exchangers between the ground and superstructures can potentially induce variable thermal axial stresses and displacements in piles.Traditional energy pile analysis methods often rely on deterministic and homogeneous soil parameter profiles for investigating thermo-mechanical soil-structure interaction,without consideration of soil spatial variability,model uncertainty or statistical uncertainty associated with interpolation of soil parameter profiles from limited site-specific measurements.In this study,a random finite difference model(FDM)is proposed to investigate the thermo-mechanical load-transfer mechanism of energy piles in granular soils.Spatially varying soil parameter profile is interpreted from limited site-specific measurements using Bayesian compressive sensing(BCS)with proper considering of soil spatial variability and other uncertainties in the framework of Monte Carlo simulation(MCS).Performance of the proposed method is demonstrated using an illustrative example.Results indicate that the proposed method enables an accurate evaluation of thermally induced axial stress/displacement and variation in null point(NP)location with quantified uncertainty.A series of sensitivity analyses are also carried out to assess effects of the pile-superstructure stiffness and measurement data number on the performance of the proposed method,leading to useful insights.

EKELAND'S VARIATIONAL PRINCIPLE AND CARISTI'S FIXED POINT THEOREM IN PROBABILISTIC METRIC SPACE

The main purpose of this paper is to establish the Ekeland’s variational principle andCaristi’s fixed point theorem in probabilistic metric spaces and to give a direct simple proofof the equivalence between these two theorems in the probabilistic metric space. The resultspresented in this paper generalize the corresponding results of [9--12].

Topological entropy of sets of generic points for actions of amenable groups

Let G be a countable discrete infinite amenable group which acts continuously on a compact metric space X and let μ be an ergodic G-invariant Borel probability measure on X. For a fixed tempered F?lner sequence {Fn} in G with limn→+∞|Fn|/log n= ∞, we prove the following result:h_top^B(G_μ, {F_n}) = h_μ(X, G),where G_μ is the set of generic points for μ with respect to {F_n} and h_top^B(G_μ, {F_n}) is the Bowen topological entropy(along {F_n}) on G_μ. This generalizes the classical result of Bowen(1973).

Energy-efficient Bio-inspired Gait Planning and Control for Biped Robot Based on Human Locomotion Analysis

In this paper an experiment of human locomotion was carried out using a motion capture system to extract the human gait features. The modifiable key gait parameters affecting the dominant performance of biped robot walking were obtained from the extracted human gait features. Based on the modifiable key gait parameters and the Allowable Zero Moment Point （ZMP） Variation Region （AZR）, we proposed an effective Bio-inspired Gait Planning （BGP） and control scheme for biped robot to- wards a given travel distance D. First, we construct an on-line Bio-inspired Gait Synthesis algorithm （BGSN） to generate a complete walking gait motion using the modifiable key gait parameters. Second, a Bio-inspired Gait Parameters Optimization algorithm （BGPO） is established to minimize the energy consumption of all actuators and guarantee biped robot walking with certain walking stability margin. Third, the necessary controllers for biped robot were introduced in briefly. Simulation and experiment results demonstrated the effectiveness of the proposed method, and the gait control system was implemented on DRC-XT humanoid robot.

Multiple Solutions for a Quasilinear Second Order Differential Equation Depending on a Parameter

The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval[a,b] R{-u＇＇=（λf（x,u）＋g（u））h（u＇）,in（a,b）,u（a）=u（b）=0under ppropriate hypotheses.We exhibit the existence of at least three（weak）solutions and,and the results are illustrated by examples.