parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity in this paper the parametrically excited vibrations of an oscillator with strong cubic negative nonlinearity are analyzed the two dimensional lindstedt poincare perturbation technique applied for finding an approximate solution of linear parametrically excited systems is extended for analyzing a strong nonlinear oscillator based on the solution of a nonlinear differential equation with constant coefficients an approximative solution is introduced the transition curves and transient surfaces along which periodic solutions exist are obtained their strong dependence on the initial conditions is evident to prove the analytical solution the numerical experiment is done for certain values initial conditions and parameter values the time history diagrams for the oscillator are plotted

flat g bundles with canonical metrics on considere la relation entre la theorie invariante des actions de groupes algebriques semi simples sur des varietes algebriques complexes et le comportement de l application de moment et des donnees quantiques fournies par une structure symplectique associee on etudie un exemple de dimension infinie comprenant des fibres plats sur des varietes de riemann compactes

dynamic behavior of a bilinear hysteretic elasto plastic oscillator part ii oscillations under periodic impulse forcing abstract the dynamic response of a single degree of freedom elasto plastic oscillator with kinematic hardening is analyzed in this paper under two kinds of periodic impulse forcing a direct and b parametric in the first case impulses of constant amplitude are applied periodically to the system and the resulting motion is analyzed using eigenvalues of the linearized poincare map and a boundary curve separating the stable and unstable periodic oscillations is obtained in the forcing parameter space in the second case the impulse amplitude is proportional to the displacement of the oscillator the forced response is extremely complex in this case the motion undergoes numerous bifurcations from periodic to quasi periodic to chaos like motions

the additivity of traces in triangulated categories abstract we explain a fundamental additivity theorem for euler characteristics and generalized trace maps in triangulated categories the proof depends on a refined axiomatization of symmetric monoidal categories with a compatible triangulation the refinement consists of several new axioms relating products and distinguished triangles the axioms hold in the examples and shed light on generalized homology and cohomology theories

study on a new nonlinear parametric excitation equation stability and bifurcation anstract the parameter stability and global bifurcations of a strong nonlinear system with parametric excitation and external excitations are investigated in detail using the method of multiple scales the nonlinear system is transformed to the averaged equation the parameter stability of solution in the case of principal parametric resonance is developed based on the averaged equation the continuation algorithm is utilized to analyze the detailed bifurcation scenario as the parameter f0 is varied the results indicate that there exist two limit points and neutral saddle points finally a series of branching points were obtained by changing the parameters f0 and

weighted composition operators from the logarithmic weighted type space to the weighted bergman space in cn let w be a bounded circular strictly convex domain in c n with c 2 boundary and h w the space of all analytic functions on w let u h w and f be a holomorphic self map of w the weighted composition operator uc f on h w is defined by uc f f z u z f f z where f h w and z w let h l o g c b w b 0 c r be the logarithmic weighted type space on w and a a p w p 0 a 1 the weighted bergman space on w here we characterize the boundedness and compactness of the weighted composition operator uc f h l o g c b w a a p w

character sheaves v this paper is part of a series s 131 devoted to the study of a class g of irreducible perverse sheaves called character sheaves on a connected reductive algebraic group g the numbering of chapters sections and references will continue that of s 131 this paper is a step towards the classification of character sheaves on g one of the main results is the following one under certain assumptions there is a natural surjective map with finite fibers from g to the set of all pairs 9 c up to conjugacy by the weyl group where 9 is a tame local system on the maximal torus and c is a two sided cell in the stabilizer w of 9 in the weyl group the assumptions made on g are

non linear dynamics of gear pair systems with periodic stiffness and backlash the present work investigates dynamics of a gear pair system involving backlash and time dependent mesh stiffness in addition the system is under the action of external excitation caused by torsional moments and gear geometry errors first the equation of motion is established in a strongly non linear form then the emphasis is laid on a specific forcing frequency range corresponding to conditions of simultaneous fundamental parametric resonance and principal external resonance for these conditions several types of periodic steady state response are identified and determined by employing suitable methodologies including techniques applicable to piecewise linear systems and to oscillators with time periodic coefficients moreover these methodologies are complemented by appropriate procedures revealing the stability properties of the located periodic solutions in the second part of the work numerical results are presented these results verify the validity and effectiveness of the new analytical methodology and provide information on the gear pair dynamics first series of typical response diagrams are obtained illustrating the effect of the mesh stiffness variation the damping and the forcing parameters on the gear pair periodic response these response diagrams are accompanied by results obtained with direct integration of the equation of motion in this way it is demonstrated that for some parameter combinations the dynamical system examined can exhibit more complicated and irregular response including crises and intermittent chaos

the dynamics of a vibromachine with parametric excitation the dynamics of a vibration machine with piecewise linear elastic ties under parametric harmonic excitation is investigated different designs of elastic elements with periodically time varying elasticity are described specific non linear features of parametric oscillations in the system under study are revealed the invariance of parametric vibration regime to possible disturbance of phase co ordinates conditions of limitedness of amplitude of parametric vibrations spectral features of non linear parametric regimes etc by the utilization of these non linear effects a procedure for the design of the main parameters of a parametric vibromachine is proposed

stability and bifurcations of hysteretic systems subjected to principal parametric excitation dynamic behavior of smooth hysteretic systems subjected to harmonic parametric excitation is investigated wen s differential equation model for hysteresis which can describe a large class of hysteretic systems is used employing the piecewise power series expression for hysteresis proposed in the previous paper the method of multiple scales is applied for the case of principal parametric resonance to obtain the second order approximate solutions and their stability it is shown that the hysteretic systems are unstable inside the principal resonance region but the responses are bounded having symmetric periodic solutions it is also shown that the systems are stable outside the region even if viscous damping does not exist because of hopf bifurcation numerical integrations are also performed to illustrate the nonlinear resonant characteristics of the systems and confirmed that trivial stationary solutions and stable symmetric periodic solutions in principal resonance region bifurcate to produce a pair of non symmetric periodic solutions stability regions with regard to excitation parameters are also illustrated the theoretical and numerical results are compared to examine the validity of the present analysis

amplitude decay of damped non linear oscillators studied with jacobian elliptic functions approximate bounded solutions of the equation x bx c 1 x c 3 x 3 0 with b 0 c 1 0 and c 3 0 are developed in terms of the jacobian elliptic functions cn cd and dn the solutions are found by following the method developed by christopher in 1973 for the case with c 1 0 and c 3 0 formulas for the amplitude decay are given in two different approximations the solutions are compared with runge kutta numerical integration results and shown to be accurate for a wide range of b c 1 c 3 and initial conditions

hyperbolic mean growth of bounded holomorphic functions in the ball we consider the hyperbolic hardy class q h p b 0 p it consists of holomorphic in the unit complex ball b for which 1 and sup q r 0 p d 0 r 1 b where q denotes the hyperbolic distance of the unit disc the hyperbolic version of the littlewood paley type g function and the area function are defined in terms of the invariant gradient of b and membership of qh p b is expressed by the l p property of the functions as an application we can characterize the boundedness and the compactness of the composition operator c defined by c f f o from the bloch space into the hardy space h p b

melnikov s criteria and chaos in systems with fractional order deflection in this paper a qualitative analysis of the dynamic systems described with the second order differential equation with fractional order deflection function is considered the existence of fixed points closed orbits and the unions of fixed points and the trajectories connecting them is shown the homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form melnikov s procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function the critical parameter values for chaos are obtained analytically and proved numerically using the lyapunov exponents the bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown the phase plane diagrams and the poincare maps for certain fractional orders are obtained the control of chaos and the transformation to periodic motion is considered

nonlinear dynamic analysis of an electrical machine rotor bearing system by the optimal homotopy perturbation method in this paper an analytical technique called the optimal homotopy perturbation method ohpm is employed to study the nonlinear behaviour of an electrical machine modelled as a rotor supported by two journal bearings with nonlinear suspension the dynamics of the rotor centre and bearing centre are studied and the spatial displacements in the horizontal and vertical directions are obtained it is shown that the main strength of the ohpm is its fast convergence since after only one iteration we obtain very accurate results for a complicated nonlinear problem which proves that this method is very efficient in practice

on characterizations of bloch type hardy type and lipschitz type spaces in this paper we establish a bloch type growth theorem for generalized bloch type spaces and discuss relationships between dirichlet type spaces and hardy type spaces on certain classes of complex valued functions then we present some applications to non homogeneous yukawa pdes we also consider some properties of the lipschitz type spaces on certain classes of complex valued functions finally we will study a class of composition operators on these spaces

on operator p g φ from the logarithmic bloch type space to the mixed norm space on the unit ball the boundedness and compactness of the following recently introduced by this author integral type operatorp f gf z email protected 0 1f f tz g tz dtt email protected b where f is a holomorphic self map of the unit ball b in c n and g is a holomorphic function on b such that g 0 0 from logarithmic bloch type spaces to mixed norm spaces on b are studied in this paper

rigid and non smoothable schubert classes a schubert class in the grassmannian is rigid if the only proper subvarieties representing that class are schubert varieties the hyperplane class 1 is not rigid because a codimension one schubert cycle can be deformed to a smooth hyperplane section in this paper we show that this phenomenon accounts for the failure of rigidity in schubert classes more precisely we prove that a schubert class in g k n is not rigid if and only if the partition 1 k defining the class has a part i such that n k i 1 i and i i 1 1 under these assumptions on the parts i and i 1 determine a partial flag isomorphic to one defining a hyperplane class in another grassmannian g k n using a deformation of the hyperplane in g k n we can deform the schubert cycle otherwise the schubert class is rigid we also show that if the partition contains the partition defining a rigid and singular schubert cycle in some grassmannian as a sub partition then cannot be represented by a smooth subvariety of g k n more precisely if does not have the form 1 j1 n k i i 1 1 for j1 i j2 and i j2 for i j2 then the schubert class cannot be represented by a smooth subvariety of g k n

resonant overlap phenomena in stochastic layers of non linear hamiltonian systems with periodical excitations an accurate standard map approach instead of the approximate standard map approach is developed for the analytical prediction of the onset of a new resonant overlap forming a new resonant separatrix web in the stochastic layer this accurate approach applies to the twin well duffing oscillator for illustration of the resonant overlap phenomena in stochastic layers the excitation strengths are obtained analytically for the onset of the specified resonant separatrix webs in the stochastic layer this accurate approach gives a very good prediction compared to numerical results for the lower order resonant overlap when excitation strength is very weak the accurate and approximate standard map methods are in good agreement and the accurate one is applicable to non linear systems with strong excitations however the further improvement should be completed for a more accurate analytical prediction of the onset of a new resonant overlap in stochastic layers of non linear hamiltonian systems with periodical excitations

chaotic motion of van der pol mathieu duffing system under bounded noise parametric excitation abstract the chaotic behavior of van der pol mathieu duffing oscillator under bounded noise is investigated by using random melnikov technique a mean square criterion is used to detect the necessary conditions for chaotic motion of this stochastic system the results show that the threshold of bounded noise amplitude for the onset of chaos in this system increases as the intensity of the noise in frequency increases which is further verified by the maximal lyapunov exponents of the system the effect of bounded noise on poincare map is also investigated in addition the numerical simulation of the maximal lyapunov exponents

on blog to qlogp pullbacks abstract we characterize the boundedness and the compactness of composition operators acting on the weighted bloch space b log generalizing previous results and answering to a question of r yoneda

the response of a single degree of freedom system with quadratic and cubic non linearities to a fundamental parametric resonance abstract the response of a one degree of freedom system with quadratic and cubic non linearities to a principal parametric resonance is investigated the method of multiple scales is used to determine the equations that describe to second order the modulation of the amplitude and phase with time about one of the foci these equations are used to determine the fixed points and their stability the perturbation results are verified by integrating the governing equation with use of a digital computer and an analogue computer for small excitation amplitudes the analytical results are in excellent agreement with the numerical solutions the large amplitude responses are investigated by using both a digital and an analogue computer the cases of single and double well potentials are investigated systems with double well potentials exhibit complicated dynamic behaviors including period multiplying and demultiplying bifurcations and chaos in some cases a bifurcated response coexists with another periodic attractor and a chaotic attractor coexists with a periodic attractor long time histories phase planes poincare maps fractal basin maps and spectra of the response are presented a bifurcation diagram of many solutions in the excitation amplitude excitation frequency plane is also presented

rigidity of smooth schubert varieties in hermitian symmetric spaces in this paper we study the space z k g p r x w of effective k cycles x in g p with the homology class equal to an integral multiple of the homology class of schubert variety x w of type w when x w is a proper linear subspace p k k n of a linear space p n in g p p v we know that z k p n r p k is already complicated we will show that for a smooth schubert variety x w in a hermitian symmetric space any irreducible subvariety x with the homology class x r x w r z is again a schubert variety of type w unless x w is a non maximal linear space in particular any local deformation of such a smooth schubert variety in hermitian symmetric space g p is obtained by the action of the lie group g

chaotic motion in the resonant separatrix bands of a mathieu duffing oscillator with a twin well potential the m 1 resonant bands in the left and right potential wells are skew symmetric and the 2m 1 resonant bands of the large orbit motion are symmetric the analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach the numerical predictions of such onset and destruction are also completed by the energy increment spectrum method the sub resonance interaction occurs for strong excitations which needs to be further investigated these results are applicable to the small and large orbit motions of post buckled structure under a parametric excitation

transition curves for the quasi periodic mathieu equation in this work we investigate an extension of mathieu s equation the quasi periodic qp mathieu equation given by ddot psi delta eps cos t cos omega t psi 0 for small eps and irrational omega of interest is the generation of stability diagrams that identify the points or regions in the delta omega parameter plane for fixed eps for which all solutions of the qp mathieu equation are bounded numerical integration is employed to produce approximations to the true stability diagrams both directly and through contour plots oflyapunov exponents in addition we derive approximate analytic expressions for transition curves using two distinct techniques 1 a regular perturbation method under which transition curves delta delta omega eps are each expanded in powers of eps and 2 the method of harmonic balance utilizing hill s determinants both analytic methods deliver results in good agreement with those generated numerically in the sense that pre

averaging method using generalized harmonic functions for strongly non linear oscillators abstract an averaging method in which generalized harmonic functions are used is applied to study the approximate solutions of the strongly non linear oscillators g x e x and g x ef x t where g x is an arbitrary non linear function the method gives the approximate solutions in terms of generalized harmonic functions these functions are also periodic and are exact solutions of strongly non linear differential equations some phenomena considered include limit cycles of strongly non linear autonomous oscillators and steady state response of strongly non linear oscillators subject to weak harmonic excitation the procedure is simple and easy to apply

forelli rudin estimates carleson measures and f p q s functions abstract a classical theorem of l carleson states that the injection map from the hardy space h p into l p d is bounded if and only if the positive measure on the unit disc is a bounded carleson measure in this paper forelli rudin estimates for arbitrary positive measures on the unit disc are proved and then these estimates are applied to characterize bounded s carleson measures in terms of bloch and f p q s functions

products of integral type operators and composition operators between bloch type spaces a complete picture on the boundedness and compactness of the products of integral type operators and composition operators between bloch type spaces of holomorphic functions on the unit disk is given in this paper

on hardy bmo and lipschitz spaces of invariantly harmonic functions in the unit ball the invariantly harmonic functions in the unit ball bbb b n in bbb c n are those annihilated by the bergman laplacian delta the poisson szeg o kernel p z zeta solves the dirichlet problem for delta if f in c s n the poisson szeg o transform of f p f z int s n p z zeta f zeta d sigma zeta where d sigma is the normalized lebesgue measure on s n is the unique invariantly harmonic function u in bbb b n continuous up to the boundary such that u f on s n the poisson szeg o transform establishes loosely speaking a one to one correspondence between function theory in s n and invariantly harmonic function theory in bbb b n when n geq 2 it is natural to consider on s n function spaces related to its natural non isotropic metric for these are the spaces arising from complex analysis in the paper different characterizations of such spaces of smooth functions are given in terms of their invariantly harmonic extensions using maximal functions and area integrals as in the corresponding euclidean theory particular attention is given to characterization in terms of purely radial or purely tangential derivatives the smoothness is measured in two different scales that of sobolev spaces and that of lipschitz spaces including bmo and besov spaces 1991 mathematics subject classification 32a35 32a37 32m15 42b25

bibloch mappings and composition operators from bloch type spaces to bmoa abstract the problem of constructing functions f 1 f 2 analytic in the unit disc d of the complex plane satisfying f 1 z f 2 z 1 1 z z d is solved for a wide class of weights that includes normal weights several applications are given particularly we can generalize known characterizations on bloch bmo pullbacks

products of composition and differentiation operators from zygmund spaces to bloch spaces and bers spaces abstract the boundedness and compactness of the products of differentiation and composition operators from zygmund spaces to bloch spaces and bers spaces are discussed in this paper

dichotomous noise induced chaos in a generalized duffing type oscillator with fractional order deflection abstract the chaotic behavior of a generalized duffing type oscillator with fractional order deflection under dichotomous noise excitation is discussed in detail using the melnikov method together with mean square criterion necessary conditions for the onsets of chaos are derived it is shown that with the increase of noise transition rate the threshold of noise amplitude for chaos firstly decreases to a minimum and then increases the effects of dichotomous noise on the duffing type oscillator are also obtained by vanishing the mean largest lyapunov exponent of the oscillator this is further verified by phase portraits and time histories with numerical simulations

maximal lyapunov exponent and almost sure stability for stochastic mathieu duffing systems abstract the principal resonance of a mathieu duffing oscillator to random excitation is investigated the method of multiple scales is used to determine the equations of modulation of amplitude and phase the effects of damping detuning cubic term and magnitudes of random excitation are analyzed the explicit asymptotic formulas for the maximal lyapunov exponent is obtained the almost sure stability or instability of the stochastic mathieu duffing system depends on the sign of the maximal lyapunov exponent in the last part of the work the numerical results are obtained

approximating the escape zone for the parametrically excited pendulum the two analytical methods employs to give approximations to the escape zone both yield reasonable results the harmonic balance method is the more accurate especially at high frequency but the critical velocity criterion does have the advantage of producing a closed form analytical expression for the zone rather than solving a series of non linear equations numerically while both methods give good results it is also worth noting that although stable non rotating solutions exist below the escape zone their basins of attractions may be fractal and subject to rapid basin erosion the onset of fractal basin boundaries and the possibility of rapid basin erosion may be predicted by a melnikov analysis as in reference

multiplicities of points on a schubert variety in a minuscule gp in this paper we prove the results announced in 13 let g be a semi simple simply connected algebraic group defined over an algebraically closed field k let t be a maximal torus b a bore1 subgroup b 3 t let w be the weyl group of g let r resp r be the set of roots resp positive roots relative to t resp b let s be the set of simple roots in r let p be a maximal parabolic subgroup in g with associated fundamental weight w let w be the weyl group of p and wp be the set of minimal representatives of w w for w e wp let e w be the point and x w the schubert variety in g p associated to w in this paper we deter mine the multiplicity m w of x w at e z where e z e x w for all minuscule p s and also for p pgn g being of type c here pun denotes the maximal parabolic subgroup obtained by omitting a the determina tion of m w is done as follows let l be the ample generator of pic g p a basis has been constructed for x w l in terms of standard monomials on x w cf 16 11 i let u be the unipotent subgroup of g generated by u et r rp here r denotes the set of roots of p and u denotes the unipotent subgroup of g associated to tl e r then u e r gives an affme neighborhood of e z in g p let a be the affine algebra of u e z and a a where is the ideal of elements of a that vanish on x w n u e z let m be the maximal ideal in a h corresponding to e r then using the results of 16 111 we obtain a basis of m f this enables us to obtain an inductive formula for f the hilbert polynomial of x w at e t cf corollaries 3 8 and 4 11 and also express m w in terms of m w s x w s being the schubert divisors in x w such that e t e x w cf theorems 3 7 and 4 10 using this we

on an integral type operator from logarithmic bloch type spaces to mixed norm spaces on the unit ball let h b denote the space of all holomorphic functions on the open unit ball b of c n and email protected h b we characterize the boundedness and compactness of the following integral type operator l gf z email protected 0 1rf tz g tz dtt email protected b where rf is the radial derivative of function f from logarithmic bloch type spaces to mixed norm spaces on the unit ball

on an integral type operator from iterated logarithmic bloch spaces into bloch type spaces let h b denote the space of all holomorphic functions on the open unit ball b of c n let f f 1 f n be a holomorphic self map of b and email protected h b such that g 0 0 in this paper we study the boundedness and compactness of the following integral type operator recently introduced by xiangling zhu and the second authori f gf z email protected 0 1rf f tz g tz dtt email protected b from the iterated logarithmic bloch spaces into the bloch type spaces for the case when f z z we also obtain a sufficient and necessary condition for the boundedness of this operator from the iterated logarithmic bloch space into the little bloch type space

generalized parametric resonance in electrostatically actuated microelectromechanical oscillators this paper investigates the dynamic response of a class of electrostatically driven microelectromechanical mem oscillators the particular systems of interest are those which feature parametric excitation that arises from forces produced by fluctuating voltages applied across comb drives these systems are known to exhibit a wide range of behaviors some of which have escaped explanation or prediction in this paper we examine a general governing equation of motion for these systems and use it to provide a complete description of the dynamic response and its dependence on the system parameters the defining feature of this equation is that both the linear and cubic terms feature parametric excitation which in comparison to the case of purely linear parametric excitation e g the mathieu equation significantly complicates the system s dynamics one consequence is that an effective nonlinearity for the overall system cannot be defined instead the system features separate effective nonlinearities for each branch of its nontrivial response as such it can exhibit not only hardening and softening nonlinearities but also mixed nonlinearities wherein the response branches in the system s frequency response bend toward or away from one another near resonance this paper includes some brief background information on the equation of motion under consideration an outline of the analytical techniques used to reach the aforementioned results stability results for the responses in question a numerical example explored using simulation of a mem oscillator which features this nonlinear behavior and preliminary experimental results taken from an actual mem device which show evidence of the analytically predicted behavior practical issues pertaining to the design of parametrically excited mem devices are also considered

perverse t structure on artin stacks in this paper we develop the theory of perverse sheaves on artin stacks continuing our earlier study of lisse etale sheaves on stacks in laszlo and olsson the six operations for sheaves on artin stacks i finite coefficients publ math ihes 2008 the six operations for sheaves on artin stacks ii adic coefficients publ math ihes 2008

improvement of a krylov bogoliubov method that uses jacobi elliptic functions abstract an improved version of a krylov bogoliubov method that gives the approximate solution of the non linear cubic oscillator x c 1 x c 3 x 3 ef x x dot 0 in terms of jacobi elliptic functions is described compact general expressions are given for the time derivatives of the amplitude and phase similar to those obtained by the usual krylov bogoliubov method which gives the approximate solution in terms of circular functions these expressions are especially simple for quasilinear c3 0 and quasi pure cubic c1 0 oscillators two types of cubic oscillators have been used as examples the linear damped oscillator f x x dot x dot and the van der pol oscillator f x x dot x 2 x dot the approximate solutions of these quasilinear and quasi pure cubic oscillators are simple and accurate the influence of the non linearity on the rate of variation of the amplitude of these two types of cubic oscillators was also studied

characteristic cycles of constructible sheaves in his paper k kashiwara introduced the notion of characteristic cycle for complexes of constructible sheaves on manifolds let x be a real analytic manifold and f a complex of sheaves of c vector spaces on x whose cohomology is constructible with respect to a subanalytic strati cation the characteristic cycle cc f is a subanalytic lagrangian cycle with in nite support and with values in the orientation sheaf of x in the cotangent bundle t x the de nition of cc f is morse theoretic heuristically cc f encodes the in nitesimal change of the euler characteristic of the stalks of f along the various directions in x it tends to be di cult in practice to calculate cc f explicitly for all but the simplest complexes f on the other hand the characteristic cycle construction has good functorial properties the behavior of cc f with respect to the operations of proper direct image verdier duality and non characteristic inverse image of f is well understood ks in this paper we describe the e ect of the operation of direct image by an open embedding combining our result with those that were previously known we obtain descriptions of cc rf f and cc f f analogous to those in ks for arbitrary morphisms f x y in the semi algebraic category and complexes f with semi algebraically constructible cohomology in e ect this provides an axiomatic characterization of the functor cc at least in the semi algebraic context our arguments do apply more generally in the subanalytic case but because statements become quite convoluted we shall not strive for the greatest degree of generality as a concrete application we consider the case of the ag manifold x of a complex semisimple lie algebra g here the weyl group w of g operates

analytical predictions of chaos in a non linear rod the resonant and chaotic conditions for non dampened non linear planar rods are developed through the chirikov criterion and the subharmonic bifurcation conditions for weakly dampened non linear planar rods are also presented through the melnikov method the analytical conditions are based on a simply supported geometrically non linear planar rod model with a specific single mode response but these conditions are applicable to geometrically non linear planar rods with different supports chaos and transient motion from chaos to periodic motion in the non linear rod are simulated through the approximate rod model and they are illustrated through the poincare mapping section

determination of periodic solutions for the motion of a particle on a rotating parabola by means of the optimal homotopy asymptotic method this paper deals with the nonlinear oscillations of a particle which moves on a rotating parabola an analytic approximate technique namely optimal homotopy asymptotic method oham is employed to propose an analytic approach to solve nonlinear oscillations the validity of the oham is independent on whether or not there exist small or large parameters in the considered nonlinear equations our procedure provides us with a convenient way to optimally control the convergence of the approximate solutions an example is given and the results reveal that this procedure is very effective simple and accurate this paper demonstrates the general validity and the great potential of the oham

generic singularities of certain schubert varieties let g be a connected semisimple algebraic group b a borel subgroup t a maximal torus in b with weyl group w and q a subgroup containing b for w in w let x wq denote the schubert variety overline bwq q for y in w such that x yq subseteq x wq one knows that byq q admits a t stable transversal in x wq which we denote by cal n yq wq we prove that under certain hypotheses cal n yq wq is isomorphic to the orbit closure of a highest weight vector in a certain weyl module we also obtain a generalisation of this result under slightly weaker hypotheses further we prove that our hypotheses are satisfied when q is a maximal parabolic subgroup corresponding to a minuscule or cominuscule fundamental weight and x yq is an irreducible component of the boundary of x wq that is the complement of the open orbit of the stabiliser in g of x wq as a consequence we describe the singularity of x wq along byq q and obtain that the boundary of x wq equals its singular locus

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

differential algebra of legendrian links let the space r q p u be equipped with the standard contact form du pdq a link l r3 is called legendrian if the restriction of to l vanishes two legendrian links are said to be legendrian isotopic if they can be connected by a path in the space of legendrian embeddings consider the map r3 r2 q p u q p since the kernel of d is everywhere transverse to the kernel of the projection l of a legendrian link l is an immersed curve we say that a link l r3 is generic with respect to or generic if all self intersections of l are transverse double points given a generic legendrian link l its diagram is the curve l r2 at every crossing of which the overpassing branch the one with the larger value of u is marked it is well known that every smooth link type can be realized by a legendrian link it is shown in sect 11 that such a realization can be chosen to have a diagram with relatively few crossings the so called classical invariants of an oriented legendrian link l are defined as follows first of them is just the smooth isotopy type of l let l1 lk be the components of l the maslov number m li of li is twice the rotation number of li the thurston bennequin number li of li is the linking number between li and s li where s is a small shift along the u direction the orientation on r3 involved in the definition of the linking number is given by the form d dq dp du in terms of the diagram li is the number of double points of li counted with signs shown in fig 1 the thurston bennequin number does not depend on the orientation of li while the maslov number changes its sign when the orientation changes

on new bloch type spaces we introduce a new bloch type space so called the logarithmic bloch type space b l o g b a d on the unit disc d as the space of all holomorphic functions f on d such thatsupz d 1 z alne b a1 z b f z 0 and b 0 and present some basic properties of the space a necessary and a sufficient condition for a function with hadamard gaps to belong to the logarithmic bloch type space are given as well as some applications of these results to a composition operator

carleson sobolev measures for weighted bloch spaces abstract carleson sobolev measures for weighted bloch spaces on the unit ball of c n are described the classical carleson measures for growth spaces on special circular domains are characterized

action du groupe des tresses sur une categorie we describe how to define by generators and relations an action of the braid group on a category more generally how to define a functor from a generalized positive braids monoid corresponding to a finite coxeter group to a monoidal category applications to constructions of bondal exceptional systems and of broue michel correspondences on flag manifolds are given

construction of approximate analytical solutions to a new class of non linear oscillator equation the principle of harmonic balance is invoked in the development of an approximate analytic model for a class of nonlinear oscillators typified by a mass attached to a stretched wire by assuming that harmonic balance will hold solutions are devised for a steady state limit cycle and or limit point motion a method of slowly varying amplitudes then allows derivation of approximate solutions by determining the form of the exact solutions and substituting into them the lowest order terms of their respective fourier expansions the latter technique is actually a generalization of the method proposed by kryloff and bogoliuboff 1943

composition operators from bloch type spaces to hardy and besov spaces boundedness and compactness of composition operators from bloch type spaces to hardy spaces and analytic besov spaces are characterized by function theoretic properties of their inducing maps for the case of the bloch space the characterizations involve the hyperbolic versions of hardy and besov classes the conditions for the hyperbolic besov classes are then interpreted geometrically when the symbols are univalent and strict inclusion between different hyperbolic besov classes is shown by an example

tuneable non degenerated nonlinear parametrically excited amplifier abstract the proposed parametric amplifier scheme can be tuned to amplify a wide range of input frequencies by altering the parametric excitation with no need to physically modify the oscillator parametric amplifiers had been studied extensively although most of the work focused on amplifiers that are parametrically excited at a frequency twice the amplifier s natural frequency these amplifiers are confined to amplifying predetermined frequencies the proposed parametric amplifier s bandwidth is indeed tuneable to nearly any input frequency not bound to be an integer multiple of a natural frequency in order to tune the stiffness and induce a variable frequency parametric excitation a digitally controlled electromechanical element must be incorporated in the realization we introduce a novel parametric amplifier with nonlinearity duffing type hardening that bounds the otherwise unlimited amplitude moreover we present a multi degree of freedom system in which a utilization of the proposed method enables the projection of low frequency vector forces on any eigenvector and corresponding natural frequency of the system and thus to transform external excitations to a frequency band where signal levels are considerably higher using the method of multiple scales analytical expressions for the responses have been retrieved and verified numerically parametric studies of the amplifiers gain sensitivities and spatial projection of the excitation on the system eigenvectors were carried out analytically the results demonstrate the advantage of the proposed approach over existing schemes practical applications envisaged for the proposed method will be outlined

vibrations in a parametrically excited system abstract this paper deals with vibrations of parametrically excited non linear systems with one degree of freedom the non linearity is cubic and is of the same order as the linear terms the parametric vibrations are excited by a periodical force of jacobi elliptic type the mathematical model of the system is a special type of non linear hill s equation the analytical approximate solution of the equation is obtained applying the elliptic krylov bogolubov method method of variable phase and amplitude developed for strong non linear differential equation of duffing type it enables the regions of unbounded solution to be defined approximately the parameters of a dynamic absorber which transforms the motion to regular are calculated in this paper

compact and weakly compact composition operators from the bloch space into mobius invariant spaces we obtain exhaustive results and treat in a unified way the question of boundedness compactness and weak compactness of composition operators from the bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like bmoa q and analytic besov spaces bp in particular by combining techniques from both complex and functional analysis we prove that in this setting weak compactness is equivalent to compactness for the operators into the corresponding small spaces we also characterize the boundedness and show that it is equivalent to compactness

hyperbolic g function and bloch pullback operators the purpose of this paper is to obtain a hyperbolic version of littlewood paley g function equivalence and then use it to estimate the operator norm of bloch pullback operators

reverse estimates in growth spaces let h b d denote the space of holomorphic functions on the unit ball b d of mathbb c d given a radial doubling weight w we construct functions f g in h b 1 such that f g is comparable to w also we obtain similar results for b d d 2 and for circular strictly convex domains with smooth boundary as an application we study weighted composition operators and related integral operators on growth spaces of holomorphic functions

on the iterated logarithmic bloch space on the unit ball abstract we introduce a new space of analytic functions on the unit ball the so called iterated logarithmic bloch space b log k and study some of its properties among other features we study the boundedness and compactness of weighted composition operators on the unit disk as well as of a recently introduced integral type operator on the unit ball with i domain the iterated logarithmic bloch space b log k or the little iterated logarithmic bloch space b log k 0 and ii range the bloch type space b or the little bloch type space b 0 or the weighted space h or the little weighted space h 0

stability analysis of the non linear mathieu equation abstract the non linear mathieu equation is analyzed within the framework of the method of normal forms analytical conditions for explosive instability are obtained and expressions for the period as well as the amplitude of the stable response are derived

mobius invariant dirichlet type spaces abstract let d p be a dirichlet type space induced by a positive parameter p and a positive borel measure on the open unit disk denote by m d p the mobius invariant function space generated by d p it is known that if the measure is finite then m d p is equal to the well known mobius invariant space q p in this paper we investigate d p and m d p spaces when the measures are not necessarily finite we give the relation between m d p and the bloch space we characterize inner functions in m d p spaces we also consider a carleson measure problem for d p spaces

cauchy integral equalities and applications we study bounded holomorphic functions 7t on the unit ball bn of cn satisfying the following so called cauchy integral equalities c 7r te y 7r m 0 1 2 for some sequence ym depending on i among the applications are the ahernrudin problem concerning the composition property of holomorphic functions on bn a projection theorem about the orthogonal projection of h2 bn onto the closed subspace generated by holomorphic polynomials in it and some new information about the inner functions in particular it is shown that if we interpret bmoa bn as the dual of hi bn then the map g g o i is a linear isometry of bmoa b1 into bmoa bn for every inner function it on bn such that it 0 0

dynamic behavior of a bilinear hysteretic elasto plastic oscillator part i free oscillations abstract free oscillations of an elasto plastic oscillator with kinematic hardening are analyzed in this paper a bilinear hysteretic model is used to represent the material non linearity the coefficient of kinematic hardening is used as a problem parameter in the equations of motion by solving the governing equations on each branch of the hysteretic cycle and matching the transition conditions an iterative map is obtained for the plastic displacements the map is analyzed and a bifurcation of the system s dynamic behavior due to change in the hardening parameter is discussed a theorem is presented to identify two distinct subranges of this parameter and the dynamic behavior of the oscillator is discussed in each subrange

smoothness of the boundary values of functions bounded and holomorphic in the disk the non eucidean counterparts of hardy littlewood s theorems on lipschitz and mean lipschitz functions are considered let i p oo and 0 a 1 forf holomorphic and bounded i f i 1 in i z i 1 the condition that f z lf z i i lf z 12 0 1 i z is necessary and sufficient for f to be continuous on i z i i with the boundary function f e e aaa the hyperbolic lipschitz class furthermore the condition that thepth mean off on the circle i z l r i is 0 1 r is necessary and sufficient for f to be of the hyperbolic hardy class h p and for the radial limits to be of the hyperbolic mean lipschitz class aaw

multiple time scale analysis of hysteretic systems subjected to harmonic excitation abstract dynamic behavior of smooth hysteretic systems subjected to harmonic excitation is analyzed wen s differential equation model for hysteresis which can be applied to a large class of hysteretic systems is used a piecewise power series expression for hysteretic restoring force is derived from wen s model assuming that steady state force displacement curve draws a single loop and that the non linearity of the restoring force is weak the method of multiple scales is applied to the equation of motion by using the piecewise power series expression for the cases of primary and secondary resonance to derive the approximate solutions and the differential equations governing the amplitude and phase of the solutions phase plane trajectories resonance curves and stability limit of the solutions are obtained and compared with the results of numerical integration in order to examine the validity of the present analysis

transition curves in a parametrically excited pendulum with a force of elliptic type this article investigates the equilibria and stability of a pendulum when the support has a prescribed motion defined by an elliptic function stability charts are generated in the parameter plane for different values of the elliptic function modulus numerical integration and floquet theory are used to generate stability charts that are later obtained through harmonic balance analysis it is shown that the size and location of the instability tongues is directly linked to the elliptic function modulus comparisons are also made between the stability charts of mathieu s equation and those of the pendulum when the prescribed motion is defined by an elliptic function

legendrian knots and constructible sheaves we study the unwrapped fukaya category of lagrangian branes ending on a legendrian knot our knots live at contact infinity in the cotangent bundle of a surface the fukaya category of which is equivalent to the category of constructible sheaves on the surface itself consequently our category can be described as constructible sheaves with singular support controlled by the front projection of the knot we use a theorem of guillermou kashiwara schapira to show that the resulting category is invariant under legendrian isotopies a subsequent article establishes its equivalence to a category of representations of the chekanov eliashberg differential graded algebra we also find two connections to topological knot theory first drawing a positive braid closure on the annulus the moduli space of rank n objects maps to the space of local systems on a circle the second page of the spectral sequence associated to the weight filtration on the pushforward of the constant sheaf is the colored by n triply graded khovanov rozansky homology second drawing a positive braid closure in the plane the number of points of our moduli spaces over a finite field with q elements recovers the lowest coefficient in a of the homfly polynomial of the braid closure

integral varieties of the canonical cone structure on g p the canonical cone structure on a compact hermitian symmetric space g p is the fiber bundle open image in new window where open image in new window is the cone of the highest weight vectors under the action of the reductive part of p it is known that the cone open image in new window coincides with the cone open image in new window of the vectors tangent to the lines in g p passing through x when we consider g p as a projective variety under its homogeneous embedding into the projective space open image in new window of the irreducible representation space v of g with highest weight associated to p a subvariety x of g p is said to be an integral variety of open image in new window at all smooth points x g p equivalently an integral variety of open image in new window is a subvariety of g p whose embedded projective tangent space at each smooth point is a linear space open image in new window we prove a kind of rigidity of the integral varieties under some dimension condition after making a uniform setting to study the problem we apply the theory of lie algebra cohomology as a main tool finally we show that the dimension condition is necessary by constructing counterexamples

twisted harmonic maps and the self duality equations si m est une surface de riemann compacte on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d auto dualite associees a une representation irreductible p 1 m psl 2 c