Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra

In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR SINGULAR ELLIPTIC SYSTEMS WITH CRITICAL SOBOLEV-HARDY AND CONCAVE EXPONENTS

In this paper,we consider a singular elliptic system with both concave non-linearities and critical Sobolev-Hardy growth terms in bounded domains.By means of variational methods,the multiplicity of positive solutions to this problem is obtained.

CONCAVE BIOLOGICAL SURFACES FOR STRONG WET ADHESION

Plant leaves, insects and geckos are masters of adhesion or anti-adhesion by smartly designed refined surface structures with micro- and nano- ＇technologies＇. Understanding the basic principles in the design of the unique surface structures is of great importance in the manufacture or synthesis of micro- and nano- devices in MEMS or NEMS. This study is right inspired by this effort, focusing on the mechanics of wet adhesion between fibers having concave tips and a flat substrate via capillary forces. We show that the concave surface can effectively enhance the wet adhesion by reducing the effective contact angle of the fiber, firmly pinning the liquid bridge at its circumferential edge. A critical contact angle is identified below which the adhesion strength can achieve its maximum, being insensitive to the contact angle between the fiber and liquid. The analytical expression for the critical angle is derived. Then a tentative design for the profile of concave surfaces is proposed, considering the effects of chamfering size, deformation and buckling, etc. The effect of liquid volume on the wet adhesion of multiple-fiber system is also discussed.

MECHANICAL ANALYSIS OF CYLINDERS BEING UPSET BETWEEN SPHERICAL CONCAVE PLATEN AND CONCAVE SUPPORTING PLATE

Mechanical analysis of cylinders being upset between spherical concave platen and concave supporting plate is conducted. Rigid-plastic mechanical models for cylinders are presented. When the ratio of height to diameter, is larger than 1, there exists two-dimensional tensile stress in the deformed body, when the ratio is smaller than 1, there exists shear stress in static hydraulic zone. The former breaks through the theory that there is three-dimensional compressive stress irrespective of any ratio of height to diameter. The latter satisfactorily explains the mechanism of layer-like cracks in disk-shaped forgings and the flanges of forged gear axles. The representation of the two models makes the upsetting, theory into correct and perfect stage.

Concave Minimization for Sparse Solutions of Absolute Value Equations

Based on concave function, the problem of finding the sparse solution of absolute value equations is relaxed to a concave programming, and its corresponding algorithm is proposed, whose main part is solving a series of linear programming. It is proved that a sparse solution can be found under the assumption that the connected matrixes have range space property(RSP). Numerical experiments are also conducted to verify the efficiency of the proposed algorithm.

Simulation of thermal field induced by concave spherical transducer in multi-layer media

High intensity focused ultrasound(HIFU)therapy is an effective method in clinical treatment of tumors,in order to explore the bio-heat conduction mechanism of in multi-layer media by concave spherical transducer,temperature field induced by this kind of transducer in multi-layer media will be simulated through solving Pennes equation with finite difference method,and the influence of initial sound pressure,absorption coefficient,and thickness of different layers of biological tissue as well as thermal conductivity parameter on sound focus and temperature distribution will be analyzed,respectively.The results show that the temperature in focus area increases faster while the initial sound pressure and thermal conductivity increase.The absorption coefficient is smaller,the ultrasound intensity in the focus area is bigger,and the size of the focus area is increasing.When the thicknesses of different layers of tissue change,the focus position changes slightly,but the sound intensity of the focus area will change obviously.The temperature in focus area will rise quickly before reaching a threshold,and then the temperature will keep in the threshold range.

Error compensation on precision machine tool servo control system based on digital concave filter

It is concluded from the results of testing the frequency characteristics of the sub micron precision machine tool servo control system, that the existence of several oscillating modalities is the main factor that affects the performance of the control system. To compensate for this effect,several concave filters are utilized in the system to improve the control accuracy. The feasibility of compensating for several oscillating modalities with a single concave filter is also studied. By applying a modified Butterworth concave filter to the practical system, the maximum stable state output error remains under ±10 nm in the closed loop positioning system.

3D stability analysis method of concave slope based on the Bishop method

In order to study the stability control mechanism of a concave slope with circular landslide, and remove the influence of differences in shape on slope stability, the limit analysis method of a simplified Bishop method was employed. The sliding body was divided into strips in a three-dimensional model, and the lateral earth pressure was put into mechanical analysis and the three-dimensional stability analysis methods applicable for circular sliding in concave slope were deduced. Based on geometric structure and the geological parameters of a concave slope, the influence rule of curvature radius and the top and bottom arch height on the concave slope stability were analyzed. The results show that the stability coefficient decreases after growth, first in the transition stage of slope shape from flat to concave, and it has been confirmed that there is a best size to make the slope stability factor reach a maximum. By contrast with average slope, the stability of a concave slope features a smaller range of ascension with slope height increase, which indicates that the enhancing effect of a concave slope is apparent only with lower slope heights.

Synthesis of Octapod Cu-Au Bimetallic Nanocrystal with Concave Structure through Galvanic Replacement Reaction

We synthesized octapod Cu-Au bimetallic alloy with a concave structure by employing a replacement reaction between Au PPh3Cl and Cu nanocubes. Using the Cu nanocube as sacrificial templates, we have successfully generated high-active sites on alloy nanocrystals by carefully tuning the replacement reaction and growth. The key is to afford the proper concentration of Au PPh3Cl-TOP to the reaction solution. When the Au precursor with high concentration is injected into the galvanic replacement reaction, the growth dominated the process and hollowed octapod Cu-Au alloy was obtained. In contrast, when the concentration of the Au precursor is low, the replacement reaction can only take place at the nanocrystals, leading to generate Cu-Au nanocages. This work provides an effective strategy for the preparation of hollow bimetallic nanocrystals with high-active sites.

The Mathematical Model of Seed Movement on a Concave Profile Rib

The differential equations of movement along the concave profile of the grate, consisting of three broken lines, are integrated on Maple 9.5 under initial conditions, using separate functions, and graphs of the dependence of movement and speed over time are presented. The graphs show the patterns of change in displacement and speed at different angles, friction coefficient of seeds along grate with a broken line of a concave profile.

Investigation of cavitation bubble collapse in hydrophobic concave using the pseudopotential multi-relaxation-time lattice Boltzmann method

The interaction between cavitation bubble and solid surface is a fundamental topic which is deeply concerned for the utilization or avoidance of cavitation effect.The complexity of this topic is that the cavitation bubble collapse includes many extreme physical phenomena and variability of different solid surface properties.In the present work,the cavitation bubble collapse in hydrophobic concave is studied using the pseudopotential multi-relaxation-time lattice Boltzmann model(MRT-LB).The model is modified by involving the piecewise linear equation of state and improved forcing scheme.The fluid-solid interaction in the model is employed to adjust the wettability of solid surface.Moreover,the validity of the model is verified by comparison with experimental results and grid-independence verification.Finally,the cavitation bubble collapse in a hydrophobic concave is studied by investigating density field,pressure field,collapse time,and jet velocity.The superimposed effect of the surface hydrophobicity and concave geometry is analyzed and explained in the framework of the pseudopotential LBM.The study shows that the hydrophobic concave can enhance cavitation effect by decreasing cavitation threshold,accelerating collapse and increasing jet velocity.

A modified discrete element method for concave granular materials based on energy-conserving contact model

The development of a general discrete element method for irregularly shaped particles is the core issue of the simulation of the dynamic behavior of granular materials.The general energy-conserving contact theory is used to establish a universal discrete element method suitable for particle contact of arbitrary shape.In this study,three dimentional(3D)modeling and scanning techniques are used to obtain a triangular mesh representation of the true particles containing typical concave particles.The contact volumebased energy-conserving model is used to realize the contact detection between irregularly shaped particles,and the contact force model is refined and modified to describe the contact under real conditions.The inelastic collision processes between the particles and boundaries are simulated to verify the robustness of the modified contact force model and its applicability to the multi-point contact mode.In addition,the packing process and the flow process of a large number of irregular particles are simulated with the modified discrete element method(DEM)to illustrate the applicability of the method of complex problems.

Effect of extrusion wheel angular velocity on continuous extrusion forming process of copper concave bus bar

The continuous extrusion forming process for producing large section copper concave bus bar under different extrusion wheel angular velocities was studied by three-dimensional finite element technology based on software DEFORM-3D. The rigid-viscoplastic constitutive equation was employed in the model. The numerical simulation results show that the deformation body flow velocity in the die orifice increases gradually with the increase of the extrusion wheel angular velocity. But slippage between the rod and extrusion wheel occurs when the extrusion wheel angular velocity is high. The effective stress near the die orifice enhances gradually with increasing extrusion wheel angular velocity. High stress is concentrated in adjacent regions of the flash gap. The effective strain gradient is greater near the abutment than that near the die orifice. The effective strain of the product increases gradually with increasing extrusion wheel angular velocity. In the deformation process, the deformation body temperature increases remarkably due to friction and deformation. So the cooling is necessary in the region of the die and tools.

EXISTENCE OF MULTIPLE SOLUTIONS FOR SINGULAR QUASILINEAR ELLIPTIC SYSTEM WITH CRITICAL SOBOLEV-HARDY EXPONENTS AND CONCAVE-CONVEX TERMS

The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.

ON SEMILINEAR ELLIPTIC EQUATIONS WITH CONCAVE AND CONVEX NONLINEARITIES IN R^N

In this paper, a class of semilinear elliptic equations with sublinear and superlinear nonlinearities in R-N is studied. By making use of variational method and L-infinity estimation, the authors obtain some results about existence of multiple positive solutions and asymptotic behavior of the solutions.

MULTIPLE POSITIVE SOLUTIONS FOR QUASILINEAR ELLIPTIC PROBLEMS INVOLVING CONCAVE-CONVEX NONLINEARITIES AND MULTIPLE HARDY-TYPE TERMS

In this paper, we deal with the existence and multiplicity of positive solutions for the quasilinear elliptic problem -△pu-∑i=1^kμi｜u｜^p-2/｜x-ai｜p^u=｜u｜^p^＊-2u＋λ｜u｜^q-2u,x∈Ω,where Ω belong to R^N（N ≥ 3） is a smooth bounded domain such that the different points ai∈Ω,i= 1,2,...,k,0≤μi〈μ^-=（N-p/p）^p,λ〉0,1≤q〈p,and p^＊=p^N/N-p.The results depend crucially cn the parameters λ,q and μi for i=1,2,...,k.

Influence of depth-thickness ratio of mining on the stability of a bedding slope with its sliding surface in concave deformation

In order to study the influence of depth-thickness ratio on bedding slope stability, whose sliding surface is flexural concave in shape under mining conditions, this paper aims to study the characteristics ofdeformarion and damage of bedding sliding with depth-thickness ratios of 200：1,150：1,120：1,100：1 and 50：1 by adopting numerical simulation analysis software combined with laboratory-made ＂under the influence of mining variable sliding surface slope similar simulation test bed＂, and to propose identification methods for slope stability under the infuence of mining. The results show that mining activities under the slope reduce slope stability. With a decrease in the mining depth ratio, the influence of mining on the slope increases gradually, and the damage to the slope gradually expands, the stability of the slope grad- ually reduces, fracture occurs on the slope toe and the central fissure gradually develops to the surface, and reaches slide threshold when the depth-thickness ratio is 50：1.

The Numerical Simulation on the PBL Structure and Its Evolution over Small-Scale Concave Terrain

A high resolution, nonhydrostatic, three dimensional diagnostic PBL model over small scale concave terrain was established in this paper. A two dimensional prognostic model was developed based on the diagnostic model. The hydrostatic approximation was abandoned and the simple energy ( E e ) closure scheme was used in both models. Using the two models, characteristics of PBL structure and its evolution were fully studied. The main characteristic of the PBL is the circulation, and it fairly affects the distribution of the pollutant in the pit.

Improvement of 2.79-μm laser performance on laser diode side-pumped GYSGG/Er,Pr:GYSGG bonding rod with concave end-faces

A comparative study on the laser performance between bonding and non-bonding Er,Pr:GYSGG rods side-pumped by 970-nm laser diodes(LDs) is conducted for the thermal lensing compensation. The analyses of the thermal distribution and thermal focal length show that the bonding rod possesses a high cooling efficiency and weak thermal lensing effect compared with the conventional Er,Pr:GYSGG rod. Moreover, the laser characteristics of maximum output power, slope efficiency, and laser beam quality of the bonding rod with concave end-faces operated at 2.79 μm are improved under the high-repetition-rate operation. A maximum output power of 13.96 W is achieved at 150-Hz and 200-μs pulse width,corresponding to a slope efficiency of 17.7% and an electrical-to-optical efficiency of 12.9%. All results suggest that the combination of thermal bonding and concave end-face is a suitable structure for thermal lensing compensation.

Matrix decomposition and Lagrangian dual method for discrete portfolio optimization under concave transaction costs

In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Computational results are reported for test problems with the data randomly generated and those from the US stock market.