compact riemannian manifolds with positive curvature operators m is said to have positive curvature operators if the eigenvalues of z are positive at each point p m meyer used the theory of harmonic forms to prove that a compact oriented n dimensional riemannian manifold with positive curvature operators must have the real homology of an n dimensional sphere gm proposition 2 9 using the theory of minimal two spheres we will outline a proof of the following stronger result

vibration characteristics of systems with multiple blades abstract an interesting phenomenon can be observed when the state space dynamic substructural method is applied to the eigenproblem of bladed disk shaft systems whether or not the shaft is flexible each frequency of the single root fixed blade appears as a frequency of the whole structure with a multiplicity of at least n 3 wheren is the number of repetitive blades the presented result can be regarded as an extension of previous findings by the authors in the sense that the commonly interfaced repetitive substructures are allowed to be treated as a rigid body in modal analysis the defectiveness issue of the multiple eigenvalues arising from the repetitive substructures is also addressed examples of rotary wing models and a simplified turbine model are presented for validation together with attempting their physical explanations

minimal two spheres in kahler einstein fano manifolds abstract in this paper we show the existence of stable symplectic non holomorphic two spheres in kahler manifolds of positive constant scalar curvature of real dimension four and in kahler einstein fano manifolds of real dimension six some of the techniques used involve deformation theory of algebraic cycles

vibration of rings on a general elastic foundation the free vibration eigensolutions of a thin ring on a general elastic foundation are obtained by perturbation and galerkin analyses natural frequencies and vibration modes are determined as closed form expressions for a ring having a circumferentially varying foundation of very general description the elastic foundation consists of two orthogonal distributed springs oriented at an arbitrary inclination angle the foundation stiffnesses vary circumferentially the simple eigensolution expressions explicitly show the parameter dependencies lead to natural frequency splitting rules for degenerate unperturbed eigenvalues at both first and second orders of perturbation and identify which nodal diameter fourier components contaminate a given n nodal diameter base mode of the free ring discrete spring supports are treated as a special case where the natural frequencies are determined by five parameters nondimensional spring stiffness stiffness angle support angle number of springs and location of the springs the predicted effects of these parameters on the natural frequencies are verified numerically as an application and as the motivating problem for the study the natural frequencies and vibration modes of a ring gear used in helicopter planetary gears with unequally spaced planets are investigated

singular boundary value problems on a half line singular boundary value problems of nonlinear second order differential equations on a half line are considered the main methods used are modified upper and lower solution techniques necessary and sufficient conditions for the existence of solutions to a class of sublinear singular boundary value problems are obtained

remarks on the existence problem of positive kahler einstein metrics on introduit un invariant m qui donne un critere pour l existence de metriques de kahler einstein

submanifolds with parallel mean curvature vector in η einstein sasaki manifold abstract in this note we prove that for a 3 dimensional submanifold in an einstein 5 sasaki manifold with einstein constant a 4 if the reeb vector field is tangent to the submanifold and it has parallel mean curvature form then it is a slant submanifold furthermore if a 4 then it is either an invariant submanifold or an anti invariant submanifold

existence theory for nonlinear fredholm and volterra integral equations on half open intervals in this chapter we present existence theory for the nonlinear fredholm integral equation y t h t smallint 0 t k t s g s y s ds 4 1 1 and the nonlinear volterra integral equation y t h t smallint 0 t k t s g s y s ds 4 1 2 when both are defined on the compact interval 0 t naturally we first concern ourselves with existence principles for both equations

existence of positive solutions for second order semipositone differential equations on the half line in this paper by means of constructing a special cone we obtain a sufficient condition for the existence of positive solution for semipositone singular sturm liouville boundary value problem on the half line the results obtained generalize and improve the corresponding results of zhang and liu in papers x g zhang l s liu positive solutions of superlinear semipositone singular dirichlet boundary value problems j math anal appl 316 2006 525 537 y s liu existence and unboundedness of positive solutions for singular boundary value problems on half line appl math comput 144 2003 543 556

existence of positive solutions for sturm liouville boundary value problems on the half line in this paper we establish sufficient conditions to guarantee the existence of at least one positive solution a unique positive solution and multiple positive solutions for the sturm liouville boundary value problem on the half line by using an effective operator the fixed point theorems in cone especially krasnoselskii fixed point theorem can be applied to such systems and then existence criteria are established the interesting point of the results is that the nonlinear term f can be sign changing

measurement and analysis of modulated doublet mode response in mock bladed disks the steady state response of spatially modulated doublet modes that occur in low count flexible bladed disks is investigated for the case in which the structure is driven by a harmonic travelling wave excitation source finite element simulation and modal testing of prototypical bladed disk structures demonstrate the presence of particular wavenumbers beyond the base number of nodal diameters which contaminate and distort the appearance of certain doublet modes the manner in which the natural frequency and wavenumber content of such modes shift and split as functions of the number of blades and their span angle is discussed in the light of a companion perturbation analysis for rotationally periodic structures resonance conditions are established and verified through simultaneous measurements made with a spin test stand using sensors that are placed in the rotating structure and stationary excitation frames of reference the travelling wave response components of a repeated frequency doublet mode are shown to propagate either in the same or opposite direction as the excitation source depending on whether certain algebraic relationships between the excitation order the base number of nodal diameters and the contamination wavenumbers are satisfied to the extent that such components can travel at different phase speeds and directions relative to one another the placement of sensors on the structure can be optimized to best measure the response amplitude conversely other placements can result in submaximal measurement of peak vibration amplitude over the structure

the in plane vibration of thin rings with in plane profile variations part ii application to nominally circular rings abstract geometric profile variations always exist in nominally circular rings due to limitations in the manufacturing processes such profile variations are known to lead to frequency splitting between pairs of modes which are degenerate in a perfect ring in this paper the effects of circumferential profile variations on the in plane vibration characteristics of such rings are studied using a numerical method the inner and outer ring surfaces are described in a very general way by fourier series and the rayleigh ritz method is used to obtain the natural frequencies and mode shapes results are presented for a number of example cases which include single and multiple harmonic variations in profile the relationship between the patterns of frequency splitting and the harmonic content of the ring profile is investigated and the most important causes of frequency splitting are identified

minimal surfaces in kahler surfaces and ricci curvature soit m une surface immergee dans une surface de kahler n soient p le nombre de points tangents complexes et q le nombre de points tangents anticomplexes denombres selon leur multiple cite on deduit une version locale de p q x m x ou x m est la caracteristique d euler de m et x la caracteristique d euler du fibre normal de m dans n

excitation of rotating circumferentially periodic structures abstract a circumferentially periodic structure consists of a finite number of identical substructures coupled together in identical ways to form a closed ring type structure the vibrational behaviour of such structures when rotating about the axis of structural symmetry is considered especially the forced response due to forces fixed in space it is known that for a circumferentially symmetric structure rotating about its axis of structural symmetry and excited by a force fixed in space resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is n n where is the angular velocity of rotation the deformation at these resonances consists of waves travelling backwards in relation to the direction of the structure rotation this resonance condition also holds for a circumferentially periodic structure but then additional resonance possibilities exist given by n kn n where n is the number of sub structures and k 0 1 2 these results are known to hold true for a structure fixed in space and acted upon by a rotating force in this paper these results are shown to hold true also for a rotating structure acted upon by a force distribution fixed in space both backward and forward travelling waves can be excited in those cases when the rotating structure exhibits coriolis accelerations the natural frequencies for backward 1n and forward 2n rotating mode shapes are different this well known property has a pronounced effect on the forced response due to forces fixed in space in the absence of coriolis effects the magnification factor is essentially 1 n 2 2 where is the forcing frequency due to rotation but in the presence of coriolis effects the magnification factor has the characteristics 1 1n 2n

quaternionic maps between hyperkahler manifolds quaternionic maps q maps between hyperkahler manifolds are quaternionic analogue of cauchy riemann equations between kahler manifolds we provide a necessary and sufficient condition on when a quaternionic map becomes holomorphic with respect to some complex structures in the hyperkahler 2 spheres and give examples of q maps which cannot be holomorphic when the domain is real 4 dimensional we analyze the structure of the blow up set of a sequence of q maps and show that the singular set of a stationary q map is h1 rectifiable

kahler einstein metrics and the generalized futaki invariant in 1983 futaki introduced his famous invariant this invariant generalizes the obstruction of kazdan warner to prescribing gauss curvature on s 2 cf ful l the futaki invariant is defined for any compact k ihler manifold with positive first chern class that has nontrivial holomorphic vector fields it is a lie algebraic character from the lie algebra of holomorphic vector fields into and its vanishing is a necessary condition for the existence of a k ihler einstein metric on the underlying manifold therefore it can be used to test the existence of k ihlereinstein metrics on a given compact k ihler manifold with positive first chern class an excellent reference on the futaki invariant is futaki s book fu2 until now all known nontrivial obstructions to k ihler einstein metrics come from holomorphic vector fields this suggests the following conjecture

positive solutions for three point boundary value problems for second order impulsive differential equations on infinite intervals this paper discusses the existence of positive solutions for three point boundary value problems for second order nonlinear impulsive differential equations on an infinite interval by using the diagonalization process fixed point theory and inequality techniques sufficient conditions for guaranteeing the existence of positive solutions are obtained

approximate controllability results for non densely defined fractional neutral differential inclusions with hille yosida operators abstractin this paper we mainly focused the approximate controllability results for a class of non densely defined fractional neutral differential control systems first we establish a set of suf

response of modulated doublet modes to travelling wave excitation the forced vibration of a rotationally periodic structure when subjected to travelling wave excitation is discussed with emphasis placed on the steady state response of doublet modes having either repeated or split frequencies such vibration modes have spatially modulated shapes defined by 1 the number of nodal diameters present in the limiting case of axisymmetry and 2 certain additional fourier harmonics which contaminate and distort their appearances the natural frequency and mode structure of a model periodic structure is discussed in the context of an otherwise axisymmetric disk having evenly spaced sector shaped line distributions of stiffness and inertia through perturbation analysis the contamination wavenumbers present in a doublet having repeated frequency are shown to comprise two subsets the members of which have sine and cosine coefficients of the same or of differing signs for each wavenumber in the mode shape s fourier expansion the structure of the wavenumber content is explored further with respect to the response of repeated and split doublets to a harmonic travelling wave excitation the individual fourier components comprising a modulated doublet can respond and propagate in the same direction as the excitation or opposite to it depending on the wavenumber of the excitation and the subset to which the contamination wavenumber belongs the response of the split frequency doublets and the circumstances under which travelling or standing wave responses or a blend of the two can occur in the structure s reference frame are also examined in the context of the model periodic structure the qualitative character of the response the forward or backward propagation direction of each mode s constituent wavenumber components and the phase speeds of those components are discussed in illustrative case studies

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

multiplier ideal sheaves and kahler einstein metrics of positive scalar curvature we present a method for proving the existence of kiihler einstein metrics of positive scalar curvature on certain compact complex manifolds and use the method to produce a large class of examples of compact kiihler einstein manifolds of positive scalar curvature suppose that m is a compact complex manifold of positive first chern class as is well known the existence of a kiihler einstein metric on m is equivalent to the existence of a solution to a certain complex monge ampere equation on m to solve this complex mongeampere equation by the method of continuity one needs only to establish the appropriate zeroth order a priori estimate suppose now that m does not admit a kiihler einstein metric so that the zeroth order a priori estimate fails to hold from this lack of an estimate we extract various global algebro geometric properties of m by introducing a coherent sheaf of ideals j on m called the multiplier ideal sheaf which carefully measures the extent to which the estimate fails the sheaf y is analogous to the subelliptic multiplier ideal sheaf that j j kohn introduced over a decade ago to obtain sufficient conditions for subellipticity of the d neumann problem now j is a global algebro geometric object on m and it so happens that j satisfies a number of highly nontrivial global algebro geometric conditions including a cohomology vanishing theorem in particular the complex analytic subspace v c m cut out by j is nonempty connected and has arithmetic genus zero if v is zero dimensional then it is a single reduced point while if v is one dimensional then its support is a tree of smooth rational curves the logarithmic geometric genus of m v always vanishes these considerations place nontrivial global algebro geometric restric

existence results for impulsive neutral functional integrodifferential equations with infinite delay abstract this paper is concerned with the existence of mild solutions for impulsive neutral functional integrodifferential equations with infinite delay in banach spaces the results are obtained by using the krasnoselski schaefer type fixed point theorem an example is provided to illustrate the theory

the in plane vibration of thin rings with in plane profile variations part i general background and theoretical formulation abstract this paper presents a methodology for the analysis of the free in plane vibration of thin rings with profile variations in the circumferential direction the methodology is suitable for any thin ring which is bounded by closed curves which are single valued functions of circumferential position the inner and outer profiles are expressed as fourier series thus allowing any profile to be approximated with any degree of accuracy an iterative numerical procedure for determining the true middle surface and the corresponding thickness at each cross section around the circumference is established a reduced plane stress form of novozhilov s thin shell theory is used to model the deformation mechanics of the ring the eigenvalue problem is then formulated using the rayleigh ritz method in conjunction with a harmonic series description of the displacements general expressions are presented for the corresponding mass and stiffness matrices a companion paper presents a comprehensive set of results which illustrates application of the theory

free and forced response of mistuned linear cyclic systems a singular perturbation approach abstract the effect of small deterministic parameter perturbations on the forced response of nearly periodic structures with cyclic symmetry is investigated the general methodology developed herein is applicable to any n degree of freedom strongly coupled cyclic system with two arbitrary and independent variations in system parameters that destroy the cyclic symmetry the specific system studied may be regarded as a simplified model of a strongly coupled bladed disk assembly singular perturbation methods along with modal expansion analysis are applied to gain a physical insight into the effects of parameter perturbations on the eigenvalues the eigenvectors as well as the forced response amplitudes the study shows that under appropriate conditions the splitting and veering of eigenvalues due to mistunings or small parameter variations increases the amplitude of vibration of some blades significantly compared to what would be predicted by an analysis of the perfectly tuned system furthermore modal bifurcations lead to uneven vibration amplitudes irrespective of the stiffness of the coupling springs the variations in blade amplitudes are also found to be strongly dependent on damping and the type of engine order excitation applied to the system for the same set of mistuning parameters

a variational characterization of complex submanifolds in this note we generalize our results in arezzo and sun reine angew math doi 10 1515 crelle 2013 0097 2012 to integer p currents of any degree we prove that if the mass of a current as a functional of the ambient metric has a critical or stable point in some special directions then the current is complex this holds for any dimension and codimension we also study a natural functional on the space of currents representing a fixed homology class closely related to the first derivative of the mass in our new approach detecting the deviation of a surface from being holomorphic

on improper integrals and differential equations in ordered banach spaces in this paper we study the existence of improper integrals of vector valued mappings the so obtained results combined with fixed point results in partially ordered functions spaces are then applied to derive existence and comparison results for least and greatest solutions of initial and boundary value problems in ordered banach spaces the considered problems can be singular functional nonlocal implicit and discontinuous concrete examples are also solved

kahler einstein metrics with positive scalar curvature in this paper we prove that the existence of kahler einstein metrics implies the stability of the underlying kahler manifold in a suitable sense in particular this disproves a long standing conjecture that a compact kahler manifold admits kahler einstein metrics if it has positive first chern class and no nontrivial holomorphic vector fields we will also establish an analytic criterion for the existence of kahler einstein metrics our arguments also yield that the analytic criterion is satisfied on stable kahler manifolds provided that the partial c 0 estimate posed in t6 is true

successive iteration and positive solutions for a second order multi point boundary value problem on a half line this paper deals with the existence of positive solutions for some second order multi point boundary value problem on the half line our approach is based on the fixed point theorem and the monotone iterative technique without the assumption of the existence of lower and upper solutions we obtain not only the existence of positive solutions for the problems but also establish iterative schemes for approximating the solutions

existence and unboundedness of positive solutions for singular boundary value problems on half line by constructing a special cone and using cone compression and expansion fixed point theorem this paper presents some existence results of positive solutions of singular boundary value problem bvp for short on half line for a class of second order differential equations at the same time the boundedness and unboundedness of positive solutions for bvp are considered also

boundary value problems on the half line with impulses and infinite delay this paper presents some results on the existence and uniqueness of solutions for the boundary value problems on the half line with impulses and infinite delay moreover an existence theorem of multiple solutions is obtained also the problems may be singular at the boundary

approximate controllability results for impulsive neutral differential inclusions of sobolev type with infinite delay abstractthe paper is mainly concerned with the approximate controllability results for a class of impulsive neutral differential control systems first we establish a set of sufficient conditions

boundary value problems on half line for functional differential equations with infinite delay in a banach space in this paper the monch fixed point theorem is used to investigate the existence of unbounded solutions of boundary value problem for functional differential equations with infinite delay in a banach space moreover an uniqueness theorem is obtained also

stability of harmonic maps of kahler manifolds soit m n une application harmonique stable d une surface de riemann fermee dans un espace symetrique hermitien simple compact alors est holomorphe