Generalized regular points of a C^1 map between Banach spaces

Let f be a C^1 map between two Banach spaces E and F. It has been proved that the concept of generalized regular points of f, which is a generalization of the notion of regular points of f, has some crucial applications in nonlinearity and global analysis. We characterize the generalized regular points of f using the three integer-valued （or infinite） indices M（x0）, Mc（x0） and Mr（x0） at x0 ∈ E generated by f and by analyzing generalized inverses of bounded linear operators on Banach spaces, that is, iff ＇（x0） has a generalized inverse in the Banach space B（E, F） of all bounded linear operators on E into F and at least one of the indices M（x0）, Mc（x0） and Mr（x0） is finite, then xo is a generalized regular point off if and only if the multi-index （M（x）, Me（x）, Mr（x）） is continuous at X0.

Coupled GIMP and CPDI material point method in modelling blast-induced three-dimensional rock fracture

Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.

NIS One-Temperature Dew-Point Generator Operating in the Ranae -50℃ to 0 ℃

This paper describes construction and characterization of a dew/frost -point generator developed at national institute for standards. It is intended to operate in the range from -50 ℃to 0 ℃. The air flows through a saturator controlled by a regulated flow meter. The reference dew/frost -point temperature was measured by standard platinum resistance thermometer （SPRT） connected to a resistance bridge. A comparative study between the saturator temperature of the new generator measured by SPRT and the dew/frost-point temperature of a calibrated chilled-mirror hygrometer was conducted. It helped to determine the uncertainty of saturator; this uncertainty was found to be between ±0.06℃ to -4- 0.15℃ at confidence limit of 95%.Several experiments were carried out in the mentioned range. Obtained results gave the confidence that NIS generator could be used as a primary humid air generator.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

奇异鞍点问题中广义位移分裂迭代方法的半收敛性分析

Recently,some authors(Shen and Shi,2016)studied the generalized shiftsplitting(GSS)iteration method for singular saddle point problem with nonsymmetric positive definite(1,1)-block and symmetric positive semidefinite(2,2)-block.In this paper,we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite(1,1)-block and symmetric positive semidefinite(2,2)-block,prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix.Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.

Multi-solution of Semilinear Elliptic Equation on R^N

In this paper, we give a Z 2 index theory of generalized critical point. By this theory we get a sufficient condition on the existing result of a class functional, as an example we give a new result that the equation-Δu+u=｜u｜ p-1 u, x∈R N,(1)has infinite solutions.

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.

THE GENERALIZED LOCAL HERMITIAN AND SKEW-HERMITIAN SPLITTING ITERATION METHODS FOR THE NON-HERMITIAN GENERALIZED SADDLE POINT PROBLEMS

For large and sparse saddle point problems, Zhu studied a class of generalized local Hermitian and skew-Hermitian splitting iteration methods for non-Hermitian saddle point problem [M.-Z. Zhu, Appl. Math. Comput. 218 （2012） 8816-8824 ]. In this paper, we further investigate the generalized local Hermitian and skew-Hermitian splitting （GLHSS） iteration methods for solving non-Hermitian generalized saddle point problems. With different choices of the parameter matrices, we derive conditions for guaranteeing the con- vergence of these iterative methods. Numerical experiments are presented to illustrate the effectiveness of our GLHSS iteration methods as well as the preconditioners.

A New Approach to Simulate Positional Error of Line Segment in GIS

To determine the distribution of positional error of a line segment, Monte Carlo approach is applied to simulate the probability density function of a line segment with the assumption that the error of endpoints in a line segment follows a two-dimensional normal distribution. For such purpose, a stochastic generator used for uncertain endpoints with the two-dimensional normal distribution is presented. This forms the basis of the generation of random line segment for the simulation of the error model of a whole line segment. The error models cover the cases where two endpoints are either independent or dependent to each other, also including a special case that the distance between two random endpoints in a line segment is close enough.

On Fatou Type Convergence of Convolution Type Double Singular Integral Operators

In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].

Henig Proper Efficient Points and Generalized Henig Proper Efficient Points

Applying the theory of locally convex spaces to vector optimization, we investigate the relationship between Henig proper efficient points and generalized Henig proper efficient points. In particular, we obtain a sufficient and necessary condition for generalized Henig proper efficient points to be Henig proper efficient points. From this, we derive several convenient criteria for judging Henig proper efficient points.

Existence of Solutions of Generalized Quasi-Variational Relation Problems by the Inductive Relations and Some Applications

By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other papers.As applications,some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.

Multiplicity of Periodic Bouncing Solutions for Sublinear Damped Variation Systems via Nonsmooth Variational Methods

Two results about the multiplicity of nontrivial periodic bouncing solutions for sublinear damped vibration systems-x=g(t)x+f(t,x) are obtained via the Generalized Nonsmooth Saddle Point Theorem and a technique established by Wu Xian and Wang Shaomin.Both of them imply the condition "f≥0" required in some previous papers can be weakened,furthermore,one of them also implies the condition about ■F(t,x)/■t required in some previous papers,such as "|■F(t,x)/■t|=σ_(0)F(t,x)" and "|■F(t,x)/■t|≤C(1+F(t,x))", is unnecessary,where F(t,x):=∫_(0)~xf(t,x)ds,and σ_(0),C are positive constants.

The Alternative Property and Vector Optimization Problem in Ordered Locally Convex Topological Vector Spaces

In this paper, the theorem of the alternative based on separation functions in ordered locally convex topological vector spaces has been established by using the concept on set valued mappings. The optimality conditions in ref. for D convex function have been generalized to ordered locally convex topological vector space and the similarly optimality conditions for D subconvexlike functions, such as the necessary and sufficient conditions of nondominated solutions, the generalized saddle point theorems and the lagrange duality theorems, have been obtained.