A THEOREM ON PLURICANONICAL MAPS OF NONSINGULAR MINIMAL THREEFOLDS OF GENERAL TYPE

51.IntroductionandtheMainTheoremLetXbeacomplexnonsingularminimalprojectivethreefoldofgeneraltype.ThenatureofpluricanonicalmapsofXisveryimportanttotheclassificationtheory.Itiswell-knownfrom[10]that4linK.lisabirationalmapform27.In[3],itisprovedthat6-canonicalmapofXisabirationalmapontoitsimage.Inthispaper,wemainlystudythefollowingproblem:Problem.WhatisthegreatestpositiveintegercosuchthatImoKxliscomposedOjapencilOjsudecesforsomeX,i.e.,dim4Im.H.I(X)=1?Benv.ni,te[1]provedthatmo53.Wecaneasily…     

On the hyperbolicity of flows

Let X be a C~1 vector field on a compact boundaryless Riemannian manifold M(dim M≥2),and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = E~sX E~u with E~s uniformly contracting and E~u uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.     

REGULARITY OF SUPERMARTINCALES INDEXED BY A LATTICE-ORDERED SET

Let X= {x_t; t∈T} be a supermartingale (resp. martingale) defined on a probability space (Ω,(?), P) with respect to (?), where (?)={(?)_t; t∈T} is nondecreasing family of sub-σ-algebras of (?). It is well known that (see Theorem 2.27 in [1] ) when T=(?)= {0, 1, …,∞}, the supermartingale (resp. martingale) X possesses the (?)-regularity, i.e., for every τ,σ∈(?) such that τ≤σ,     

A topological position of the set of continuous maps in the set of upper semicontinuous maps

Let (X, ρ) be a metric space and ↓USCC(X) and ↓CC(X) be the families of the regions below all upper semi-continuous compact-supported maps and below all continuous compact-supported maps from X to I = [0, 1], respectively. With the Hausdorff-metric, they are topological spaces. In this paper, we prove that, if X is an infinite compact metric space with a dense set of isolated points, then (↓USCC(X), ↓CC(X)) ≈ (Q, c0 ∪ (Q \ Σ)), i.e., there is a homeomorphism h :↓USCC(X) → Q such that h(↓CC(X)) = c0 ∪ (Q \ Σ...     

A strong approximation of self-normalized sums

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.     

A self-normalized law of the iterated logarithm for the geometrically weighted random series

Let {X, X_n; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX~2I(|X| ≤ x) is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞_(n=0)β~nX_n(0 β 1) is obtained, under some minimal conditions.     

DIFFERENTIAL INEQUALITIES OF OPERATOR-VALUED ANALYTIC FUNCTIONS

1 IntroductionLet H dellote a colllplex Hilbert space. Let B(H) be a co1llplex Banach space of all boundedliuear operators on H, alld B(H)*, tl1e co11jugate space of B(H). The real and inlaginary partsrof all operator T on H are denoted by ReT and IlllT, respectively, i.e., ReT = op, I111T =ng. A contraction is a11 operator T E B(H) with 11TI1 5 1, a proper contractioll is al1operator T 6 B(H) witl1 lITlI < 1.We say that f is all operator-val[1ed fullction on the u1lit disc A = {…     

Englixh An Interior Point Algorithm forthe Parametric Linear Complementarity Problem

1.IntroductionLetLCP[t]:S~MX q tq,S20,X20,STX~0bealinearcomplementarityproblem(LCP)withtERasitsparameter.Inthispaper,theproblemisassumedtobemonotone,i.e.,MEboxsispositivesemi-definite.Itisalsoassumedthattheproblemisnon-trivial,i.e.,thereexistsatERsuc...     

NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS

§1.IntroductionLet(?,F)be a measurable space and let Lb(F)be the space of F-measurable andbounded real functions.A nonlinear expectation is a continuous functionalE[·]:Lb(F)?→Rthat is order preserving(i.e.,E[X1]≥E[X2],if X1≥X2)and constant preserving     

Maximal function characterizations of Hardy spaces on RD-spaces and their applications

Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a dimension n. For α∈ (0, ∞) denote by Hαp(X ), Hdp(X ), and H?,p(X ) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calder′on reproducing formula, it is shown that all these Hardy spaces coincide with Lp(X ) when p ∈ (1, ∞] a...     

Iterative solution of nonlinear equations of accretive and pseudocontractive types

Let E be a real uniformly smooth Banach space. Let A:D(A)=E→2E be an accretive operator that satisfies the range condition and A⁻¹(0)≠∅. Let {λ_n} and {θ_n} be two real sequences satisfying appropriate conditions, and for z∈E arbitrary, let the sequence {x_n} be generated from arbitrary x₀∈E by x_n+1=x_n−λ_n(u_n+θ_n(x_n−z)), u_n∈Ax_n, n?0. Assume that {u_n} is bounded. It is proved that {x_n} converges strongly to some x∗∈A−1(0). Furthermore, if K is a nonempty closed convex subset of E and T:K→K is a bounded continuous pseudocontractive map with F(T):={Tx=x}≠∅, it is proved that for arbitrary z∈K, the sequence {x_n} generated from x₀∈K by x_n+1=x_n−λ_n((I−T)x_n+θ_n(x_n−z)), n?0, where {λ_n} and {θ_n} are real sequences satisfying appropriate conditions, converges strongly to a fixed point of T.     

Characterizations of relatively generalized monotone maps

New concepts of relative monotonicity were introduced in Konnov (Oper Res Lett 28:21–26, 2001a) which extend the usual ones. These concepts enable us to establish new existence and uniqueness results for variational inequality problems over product sets. This paper presents first-order characterizations of new (generalized) monotonicity concepts. Specialized results are obtained for the affine case.      

On the uniform hyperbolicity of some nonuniformly hyperbolic systems

We give sufficient conditions for the uniform hyperbolicity of certain nonuniformly hyperbolic dynamical systems. In particular, we show that local diffeomorphisms that are nonuniformly expanding on sets of total probability (probability one with respect to every invariant probability measure) are necessarily uniformly expanding. We also present a version of this result for diffeomorphisms with nonuniformly hyperbolic sets.

     

Nielsen fixed point theory for partially ordered sets

In this paper, we introduce a Nielsen type number for any selfmap f of a partially ordered set of spaces. This Nielsen theory relates to various existing Nielsen type fixed point theories for different settings such as maps of pairs of spaces, maps of triads, fibre preserving maps, equivariant maps and iterates of maps, by exploring their underlying poset structures.     

Duality Results for Generalized Vector Variational Inequalities with Set-Valued Maps

In this paper, we introduce new dual problems of generalized vector variational inequality problems with set-valued maps and we discuss a link between the solution sets of the primal and dual problems. The notion of solutions in each of these problems is introduced via the concepts of efficiency, weak efficiency or Benson proper efficiency in vector optimization. We provide also examples showing that some earlier duality results for vector variational inequality may not be true. This work was supported by the Brain Korea 21 Project in 2006.     

Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family

We consider quasisymmetric reparametrizations of the parameter space of the quadratic family. We prove that the set of quadratic maps which are either regular or Collet-Eckmann with polynomial recurrence of the critical orbit has full Lebesgue measure, for any such reparametrization.     

The stress-energy tensor for biharmonic maps

Using Hilbert’s criterion, we consider the stress-energy tensor associated to the bienergy functional. We show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four. First, we use this tensor to construct new examples of biharmonic maps, then classify maps with vanishing or parallel stress-energy tensor and Riemannian immersions whose stress-energy tensor is proportional to the metric, thus obtaining a weaker but high-dimensional version of the Hopf Theorem on compact constant mean curvature immersions. We also relate the stress-energy tensor of the inclusion of a submanifold in Euclidean space with the harmonic stress-energy tensor of its Gauss map. S. Montaldo was supported by PRIN-2005 (Italy): Riemannian Metrics and Differentiable Manifolds. C. Oniciuc was supported by a CNR-NATO (Italy) fellowship and by the Grant CEEX, ET, 5871/2006 (Romania).     

On quasiregular mappings between smooth Jordan domains

It is proved that every proper quasiregular C² mapping w between two plane Jordan domains Ω∈C1,α and G∈C2,α, 0<α?1, satisfying the differential inequality |Δw|?M²|∇w|+N is Lipschitz continuous. This extends the main result of the author and M. Mateljevi? (Kalaj and Mateljevi?, 2006 [7]).     

Finite Degree Holomorphic Covers of Compact Riemann Surfaces

A conjecture of Ehrenpreis states that any two compact Riemann surfaces of genus at least two have finite degree unbranched holomorphic covers that are arbitrarily close to each other in moduli space. Here we prove a weaker result where certain branched covers associated with arithmetic Riemann surfaces are allowed, and investigate the connection of our result with the original conjecture.