On path-independent integrals in three-dimensional nonlinear fracture dynamics

This paper deals with the path-independent integrals in non-linear three-dimensional fracture dynamics.Both the nonli-near elastic case and the elastic-plastic case are considered,and some path-independent integrals have been worked out.Forexplaining the physical meaning of these integrals,a speci-men with plane notch is considered,and the relation betweenthe integral and dynamical crack extension force is establish-ed.Thus.such integrals may serve as a fracture criterionin nonlinear fracture dynamics.     

Quasi-weak convergence with applications in ordered Banach space

Ｉｔｉｓｗｅｌｌ＿ｋｎｏｗｎｔｈａｔｔｈｅｔｈｅｏｒｙｏｆｍｏｎｏｔｏｎｅｓｅｑｕｅｎｃｅａｎｄｆｉｘｅｄｐｏｉｎｔｓｉｎｏｒｄｅｒｅｄＢａｎａｃｈｓｐａｃｅｉｓａｎｉｍｐｏｒｔａｎｔｔｏｏｌｆｏｒｉｎｖｅｓｔｉｇａｔｉｎｇｔｈｅｎｏｎｌｉｎｅａｒｐｒｏｂｌｅｍ．Ｕｔｉｌｉｚｉｎｇｔｈｉｓｔｏｏｌ,ｃｏｎｔｉｎｕｉｔｙａｎｄｃｏｍｐａｃｔｎｅｓｓａｒｅｕｓｕａｌｌｙａｓｓｕｍｅｄ（ｓｅｅ［１～３］）．Ｒｅｃｅｎｔｌｙ,ｗｉｔｈｏｕｔｔｈｅｓｕｐｐｏｓｅｏｆｃｏｎｔｉｎｕｉｔｙ,ｔｈｅｅｘｉｓｔｅ…     

Constraint-induced restriction and extension operators with applications

The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.     

Fixed point index of uniform limit of set-Valued strict set-contractive mappings and its applications

In this paper,the class of uniform limit mappings of set-valued,strick set-contractivemappings is discussed.Furthermore,the fixed point index theory for the uniform limitmappings is established.Using the fixed point index theory,some positive fixed pointtheorems are proved.Our theorems generalize some results in[1,4,5,7].     

On probabilistic norm of a linear operators and space of operators

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］,ＸｉａｏｉｎｔｒｏｄｕｃｅｄｔｈｅｎｏｔｉｏｎｏｆｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｏｆａｌｉｎｅａｒｏｐｅｒａｔｏｒｏｎＭｅｎｇｅｒｐｒｏｂａｂｉｌｉｓｔｉｃｎｏｒｍｅｄｓｐａｃｅ（ｂｒｉｅｆｙ,ＭｅｎｇｅｒＰＮ＿ｓｐａｃｅ）．Ａｎｄｂｙｕｓｉｎｇｔｈｅｎｏｔｉｏｎ,ｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｏｆｔ＿ｎｏｒｍΔｓａｔｉｓｆｙｉｎｇΔ（ｔ,ｔ）≥ｔ（ｔ∈（０,１］）,ｈｅｇａｖｅａｄｅｓｃｒｉｐｔｉｏｎｏｆｂｏｕｎｄｅｄｎｅｓｓｏｆｌｉｎｅａｒｏｐｅ…     

Caristi type hybrid fixed point theorems in menger probabilistic metric space

I.IntroductionandPreliminariesInl976,CaristiprovedtheCaristi'sfixedpointtheoreminIll.Becausethistheoremdoesnotrequirethecontinuityofthemapping.ittindsapplicationsinmanyfields.Inl99l,S.S.Changetal.l'l,broughtforwardCaristi'sfixedpointtheoremandEkeland'svar…     

Probabilistic norm of linear operators on PN space

I.IntroductionInl4],adefinitionofprobabilisticnormoflinearoperatorsonMengerprobabiIisticnormedlinearspace(brieflyM-PNspace)wasgiven.Itissuperiortoeachdefinitionin[l],I5J,I6],I7j,becausetheboundednessoflinear0peratorscanbedescribedwellbymeansofit.Thispaper…     

Existence and stability of common fixed points for systems of mappings

In this paper,we establish some common fixed point theorems and stability theorems of the sets of common fixed points for the systems of set-valued and single-valued nonlinear contractive type mappings in a finite Cartesian product of metric spaces.     

On the boundary value problems for ordinary differential equations with turning points

In this paper,we consider the boundary value problems of the formsy″-f(x,ε)y′ g(x,ε)=0 (-a≤x≤b,0≤ε《1 )y(-a)=a,y(b)=βwhere f(x,0)has several and multiple zeros on the interval[-a,b].The conditions forexhibiting boundary and interior layers are given,and the corresponding asymptoticexpansions of solutions are constructed.     

Fixed points of a pair of asymptotically regular mappings

I.IntroductionTheconceptofasymptoticregularitywasintroducedbyBrowderandPetryshynl'].LetEbearealBanachspacewithnorn11l'l'AmappingT:E-Eissaidtobeasymptotical1yregulariflimijT" 'x~T'x:l=ofora1lxinE,whereTffxdenotesthenthiteratio11of--ooT.ltiswell-knownthatif…     

Minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces

In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikanthamt and the results obtained by Lan in, and.     

FIXED POINT THEOREMS FOR FUZZY MAPPINGS IN PROBABILISTIC METRIC SPACES

ＦＩＸＥＤ　ＰＯＩＮＴ　ＴＨＥＯＲＥＭＳ　ＦＯＲ　ＦＵＺＺＹ　ＭＡＰＰＩＮＧＳ　ＩＮ　ＰＲＯＢＡＢＩＬＩＳＴＩＣ　ＭＥＴＲＩＣ　ＳＰＡＣＥＳＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）；ＺｈａｎｇＹｉｎｇ（张颖）；ＹｕａｎＪｉａｗｅｉ（袁家玮）（Ｒｅｃｅｉｖ...     

On uniform convergence of linear operators on the probabilistic normed space

In this paper, we introduced the notion of uniform convergence of the linear operators on the probabilistic normed space, and the notion of probabilistic distance between the operators, which describes the above convergence completely. In terms of these notions, we obtained the essential features of the continuity of operators, and of the uniform convergence of operator sequences, and we also obtained the closure of continuity and complete continuity under the operation of the limit of uniform convergence.     

Features of the stress field near tunnel inclusions in an inhomogeneous anisotropic space

This paper proposes a method to solve problems for interface tunnel defects in a piecewise-homogeneous elastic material that is under generalized plane strain and has no planes of elastic symmetry. The method is based on integral relations between the discontinuities and sums of the components of the displacement vector and stress tensor at the interface. Closed-form solutions are obtained for a system of interface tunnel inclusions with mixed contact conditions between the space and the inclusions. The dependences of the indices of singularity of the solutions on orthogonal coordinate transformation are established for different combinations of materials of monoclinic and orthorhombic systems. The effect of the antiplane component on the behavior of the solutions is revealed __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 6, pp. 36–45, June 2008.     

Nonempty intersection theorems in topological spaces with applications

In this paper, we establish some new nonempty intersection theorems for generalized L-KKM mappings and prove some new fixed point theorems for set-valued mappings under suitable conditions in topological spaces. As applications, an existence theorem for an equilibrium problem with lower and upper bounds and two existence theorems for a quasi-equilibrium problem with lower and upper bounds are obtained in topological spaces. Our results generalize some known results in the literature.     

Fixed point theorems of local contraction mappings on menger spaces

In this paper,we introduce the concept ofε-chainable PM-space,and give severalfixed point theorems of one-valued and multivalued local contraction mapping on the kindof spaces.     

Positive Solutions of Boundary Value Problems for Second-Order Singular Nonlinear Differential Equations

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ,ｗｅｓｈａｌｌｃｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｓｉｎｇｕｌａｒｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓ (ＢＶＰ)ｕ″ ｇ(ｔ)ｆ(ｕ) =0 ,　　 0 <ｔ<1 ,αｕ(0 ) -βｕ′(0 ) =0 ,　　γｕ(1 ) δｕ′(1 ) =0 ,(1 )ｗｈｅｒｅα ,β,γ ,δ≥ 0 ,ρ:=βγ αγ αδ>0 ,ｆ∈Ｃ([0 ,∞ ) ,[0 ,∞ ) ) ,ｇｍａｙｂｅｓｉｎｇｕｌａｒａｔｔ=0ａｎｄ/ｏｒｔ=1 .Ｔｈｉｓｐｒｏｂｌｅｍａｒｉｓｅｓｎａｔｕｒａｌｌｙｉｎｔｈｅｓｔｕｄｙｏｆｒａｄｉａｌｌｙｓｙｍｍｅｔ…     

The explicit forms of field functions in totrahedron element with 16 and 20 degrees of freedom

In this paper, the explicit forms of field functions in tetrehedron elements with 16 and 20 degrees of freedom are given in terms of volume coordinatesL ₁,L ₂,L ₃,L ₄ of tetrahedron.     

The index of lyapunov stable fixed points in two dimensions

In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR ₂ has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.     

On the periodic solutions of differential inclusions and applications

The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semi-linear differential inclusion. An application to some feedback control systems isdiscussed.