complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

the weil petersson hessian of length on teichmuller space we present a brief but nearly self contained proof of a formula for the weil petersson hessian of the geodesic length of a closed curve either simple or not simple on a hyperbolic surface the formula is the sum of the integrals of two naturally defined positive functions over the geodesic proving convexity of this functional over teichmuller space due to wolpert 1987 we then estimate this hessian from below in terms of local quantities and distance along the geodesic the formula extends to proper arcs on punctured hyperbolic surfaces and the estimate to laminations wolpert s result that the thurston metric is a multiple of the weil petersson metric directly follows on taking a limit of the formula over an appropriate sequence of curves we give further applications to upper bounds of the hessian especially near pinching loci recover through a geometric argument wolpert s result on the convexity of length to the half power and give a lower bound for growth of length in terms of twist

spherical functions on symmetric cones in this note we obtain a recursive formula for the spherical functions associated with the symmetric cone of a formally real jordan algebra we use this formula as an inspiration for a similar recursive formula involving the jack polynomials

invariant functions on lie groups and hamiltonian flows of surface group representations si est le groupe fondamental d une surface orientee fermee s et g est un groupe de lie satisfaisant des conditions tres generales alors l espace hom g g des classes de conjugaison de representation g a une structure symplectique naturelle on etudie la geometrie de cette structure symplectique a l aide d une famille naturelle de fonctions sur hom g g

periodic solutions of higher order delay differential equations abstract in this paper we prove existence results for periodic solutions concerning the higher order delay differential equations our method is based upon the coincidence degree theory of mawhin the results obtained are new examples are given to illustrate the main results

behavior of geodesic length functions on teichmuller space let t be the teichmuller space of marked genus g n punctured riemann surfaces with its bordification t the augmented teichmuller space of marked riemann surfaces with nodes abi77 ber74 pro vided with the wp metric t is a complete cat 0 metric space dw03 wol03 yam04 an invariant of a marked hyperbolic struc ture is the lengthof the geodesic in a free homotopy class a basic feature of teichmuller theory is the interplay of two dimensional hyperbolic geometry weil petersson wp geometry and the behavior of geodesic length functions our goal is to develop the understanding of the intrinsic local wp geometry through a study of the gradient and hessian of geodesic length functions considerations include ex pansions for the wp pairing of gradients expansions for the hessian and covariant derivative comparability models for the wp metric as well as the behavior of wp geodesics including a description of the alexandrov tangent cone at the augmentation approximations and applications for geodesics close to the augmentation are developed an application for fixed points of group actions is described bound ing configurations and functions on the hyperbolic plane is basic to our approach considerations include analyzing the orbit of a dis crete group of isometries and bounding sums of the inverse square exponential distance

a hopf bifurcation for a reaction diffusion equation with concentrated chemical kinetics abstract a reaction diffusion equation related to some mathematical models of gasless combustion of solid fuel is studied a formal bifurcation analysis by b j matkowsky and g i sivashinsky siam j appl math 35 1978 465 478 shows that solutions demonstrate behavior typical for the hopf bifurcation a rigorous treatment of this phenomenon is developed the problem is considered as an evolution equation in a banach space to circumvent difficulties involving a possible resonance with the continuous spectrum appropriate weighted norms are introduced a suitable version of the hopf bifurcation theorem is developed and the existence of time periodic solutions is proved for values of the parameter near some critical value

on the symplectic geometry of deformations of a hyperbolic surface let r be a riemann surface in this manuscript we consider a geometry on the moduli space x r for r which we regard as the space of equivalence classes of constant curvature metrics on the underlying smooth manifold of r classically the space of flat metrics for a torus is the locally symmetric space 0 2 sl 2 r sl 2 z we shall describe a symplectic geometry for the space of hyperbolic metrics on a surface of negative euler characteristic the teichmiiller space t r a covering of the moduli space is a complex kihler manifold a kuhler metric for t r defined in terms of the petersson product for automorphic forms was introduced by weil 1 the weil petersson metric is invariant under the covering transformations and so projects to the moduli space x r the metric provides a link between the function theory of r and the geometry of x r in the fenchel nielsen manuscript 8 a deformation based on an amalgamation construction for fuchsian groups is introduced the deformation is defined geometrically by cutting the surface along a simple closed geodesic rotating one side of the cut relative to the other and attaching the sides in their new position the hyperbolic metric in the complement of the cut extends to a hyperbolic metric on the new surface choose a free homotopy class a on the surface r then for each marked surface r realize a by the closed geodesic ar the fenchel nielsen deformations for the athen define a 1 parameter group of diffeomorphisms of t r whose infinitesimal generator by definition is the fenchel nielsen vector field ta in 21 the fenchel nielsen deformation was described in terms of quasiconformal mappings and an investigation of the vector fields t was begun the fenchel nielsen vector fields were found to be related to the geodesic length functions 1 introduced by fricke klein to provide coordinates for t r

defuzzification criteria and classification in this paper we contribute to the theory and development of defuzzification techniques first we define the core of a fuzzy set then we formulate a set of criteria for defuzzification in arbitrary universes ordered universes and the set of the real numbers finally we classify the most widely used defuzzification techniques into different groups and we examine the prototypes of each group with respect to the defuzzification criteria we show that the maxima methods behave well with respect to the more basic defuzzification criteria and hence are good candidates for fuzzy reasoning systems on the other hand the distribution methods and the area methods do not fulfill the basic criteria but they exhibit the property of continuity that makes them suitable for fuzzy controllers

a bayesian approach to managing learning curve uncertainty this paper introduces a bayesian decision theoretic model of optimal production in the presence of learning curve uncertainty the well known learning curve model is extended to allow for random variation in the learning process with uncertainty regarding some parameter of the variation a production run generates excess value above its current revenue for a bayesian manager in two ways it pushes the firm further along the learning curve increasing the likelihood of lower costs for future runs and it provides information through the observed costs that reduces the uncertainty regarding the rate at which costs are decreasing we provide conditions under which one of the classical deterministic learning curve results namely that optimal production exceeds the myopic level carries over to the extended framework we demonstrate that another classical deterministic learning curve result namely that optimal production increases with cumulative production does not hold in the bayesian setting

periodic boundary value problems for second order impulsive differential systems on etudie le probleme aux valeurs limites periodiques pour un systeme d equations differentielles d ordre 2 faiblement couplees avec impulsion

applying fuzzy set approach to signal detection theory abstract the fuzzy set theory is applied to the signal detection theory to develop a new approach called the fuzzy signal detection theory fsdt first linguistic variables are provided for the observer to describe his belief about the presence of a signal then based on the assumptions that the judgment criterion xc and sensitivity d are both fuzzy we use fuzzy integration to derive their membership functions and thus give a more reasonable description of the signal detection mechanism further a new index called the stability is proposed to investigate the consistency property of human judgment it can be used as a selection criterion for signal detection personnels finally some defuzzification operations are performed to put these results into use and to develop a new tool for system comparison i e the fuzzy receiver operating characteristic froc curve the fuzzy set approach is found to be more efficient and effective than the traditional roc curve

the polyakov path integral over bordered surfaces the open string amplitudes we use the feynman functional quantization scheme adapted to the gauge theories with reparametrization invariance to the functional covariant first quantization of the open bosonic bdhp string in a position representation the consistent functional integral representation of the open string propagator is derived and evaluated this result is used as a starting point for two kinds of constructions of the off shell multiloop open string amplitudes the general idea of the presented approach is to consider the off shell amplitudes as functionals on the space of contours endowed with an intrinsic metric or on the space

an analytic construction of the deligne mumford compactification of the moduli space of curves in 1969 p deligne and d mumford compactified the moduli space of curves their compactification is a projective algebraic variety and as such it has an underlying analytic structure alternatively the quotient of the augmented teichmueller space by the action of the mapping class group gives a compactification of the moduli space we put an analytic structure on this compact quotient and prove that with respect to this structure it is canonically isomorphic as an analytic space to the deligne mumford compactification

hukuhara kneser property for a nonlinear dirichlet problem abstract the purpose of this paper is to show that the set of solutions of a nonlinear dirichlet problem satisfies the usual hukahara kneser property for ordinary differential equations

holomorphic extensions of laplacians and their determinants the teichmuller space teich s of a surface s in genus g 1 is a totally real submanifold of the quasifuchsian space qf s we show that the determinant of the laplacian det on teich s has a unique holomorphic extension to qf s to realize this holomorphic extension as the determinant of differential operators on s we introduce a holomorphic family of elliptic second order differential operators on s whose parameter space is the space of pairs of beltrami differentials on s and which naturally extends the laplace operators of hyperbolic metrics on s we study the determinant of this family and show how this family realizes the holomorphic extension of det as its determinant

invariant manifolds and bifurcation for quasilinear reaction diffusion systems in this paper we consider parameter dependent quasilinear reaction diffusion equations on a bounded domain of r it is our purpose to study the dynamical behavior of solutions to these equations in particular we are interested in the behavior of the solution set if the parameter is changed to be more precise let us assume that sz c r is a bounded domain having a smooth boundary then we consider the parameter dependent equation

solvability of periodic boundary value problems for nth order ordinary differential equations in this paper we prove existence results for periodic boundary value problems concerning the n t h order differential equationx n t f t x t x t x n 1 t t 0 1 our method is based upon the coincidence degree theory of mawhin the results obtained are new examples are given to illustrate the main results

nonlinear second order periodic boundary value problems abstract in this paper we study a periodic boundary value problem pbvp for brevity of second order it is well known that if and are upper and lower solutions respectively with then there exists a solution u such that u when nothing was known the main purpose of this paper is to consider this last case also we study the structure of the set of solutions of the pbvp in the sector when and we apply the results to the case

a class of nonlinear boundary value problems without landesman lazer condition is a uniformly elliptic operator over a smooth bounded domain l il is its smallest eigenvalue and p is orthogonal to the eigenfunction 4 corresponding to a we choose to study 1 1 for the sake of simplicity and clarity problems of the type 1 1 or 1 2 are referred to in the literature as nonlinear perturbations of linear boundary value problems at resonance and 1

the polyakov path integral over bordered surfaces ii the closed string off shell amplitudes following the general scheme of the convariant path integral quantization of gauge systems two alternative formulations of the first quantized closed bosonic string in a position representation are presented in both approaches the covariant path integral representations of the propagator and of the higher order off shell amplitudes are constructed for a wide class of gauges the explicit formulae for off shell amplitudes are obtained this paper is the continuation of our previous work where the corresponding problems in the open string case were considered 20

infinitesimal bending and twisting in one dimensional dynamics an infinitesimal theory for bending and earthquaking in one dimensional dynamics is developed it is shown that any tangent vector to teichmuller space is the initial data for a bending and for an earthquaking or dinary differential equation the discussion involves an analysis of infinitesimal bendings and earthquakes the hilbert transform natural bounded linear oper ators from a banach space of measures on the mobius strip to tangent vectors to teichmuller space and the construction of a nonlinear right inverse for these operators the inverse is constructed by establishing an infinitesimal version of thurston s earthquake theorem

existence of periodic solutions for first order differential equations in this paper we study the periodic boundary value problem for first order differential equations by combining techniques of the theory of differential inequalities namely the method of upper and lower solutions and the alternative method for nonlinear problems at resonance the results obtained are in terms of the behavior of the nonlinear part at infinity

periodic solutions of some lienard and duffing equations on etudie certains aspects du probleme periodique u f u u g t u 0 u 0 u 2 u 0 u 2 ou f est une fonction continue sur r et g t u est une fonction de caratheodory soumise a certaines restrictions de croissances on donne deux resultats d existence

amenability poincare series and quasiconformal maps any coveringy x of a hyperbolic riemann surfacex of finite area determines an inclusion of teichmuller spaces teich x teich y we show this map is an isometry for the teichmuller metric if the covering isamenable and contracting otherwise in particular we establish 1 for classical poincare series kra s theta conjecture

a procedure for ordering fuzzy subsets of the unit interval abstract we introduce a function to help in the ordering of fuzzy subsets of the unit interval this function is the integral of the mean of the level sets associated with the fuzzy subsets various properties of this function are studied

a fuzzy set approach for evaluating and enhancing the mid term competitiveness of a semiconductor factory fuzzy set theory is applied in this study to establish a systematic procedure for evaluating the mid term competitiveness of a semiconductor manufacturing factory subsequently to enhance the overall competitiveness of the semiconductor manufacturing factory a capacity re allocation mechanism is designed to improve the competitiveness of less competitive products without raising the expense of the other products and diminishing their competitiveness for this purpose a fuzzy nonlinear programming fnp model is constructed and is then converted into an equivalent np problem that can be solved with the existing optimization problem solving package to prove the usefulness of the proposed methodology a real case containing the data collected from a dram manufacturing factory was investigated after reallocating its capacity the competitiveness of the whole factory was indeed enhanced besides the capacity plan developed by the capacity re allocation mechanism was shown to be both efficient and practical

limits of quasi fuchsian groups with small bending we study limits of quasi fuchsian groups for which the bending measures on the convex hull boundary tend to zero giving necessary and sufficient conditions for the limit group to exist and be fuchsian as an application we complete the proof of a conjecture made in 24 conjecture 6 5 that the closures of pleating varieties for quasi fuchsian groups meet fuchsian space exactly in kerckhoff s lines of minima of length functions doubling our examples gives rise to a large class of cone manifolds which degenerate to hyperbolic surfaces as the cone angles approach 2

exotic projective structures and quasi fuchsian space ii let p s be the space of projective structures on a closed surface s of genus g 1 and let q s be the subset of p s of projective structures with quasi fuchsian holonomy it is known that q s consists of infinitely many connected components in this article we show that the closure of any exotic component of q s is not a topological manifold with boundary and that any two components of q s have intersecting closures

periodic solutions of nonlinear parabolic equations abstract in this paper we study the periodic neumann boundary value problem for semilinear parabolic equations we present some existence results and study the structure of the set of solutions giving sufficient conditions under which that solution set is compact connected or acyclic

the polyakov path integral over bordered surfaces iii the brst extended closed string off shell amplitudes the geometrical approach to the functional integral over faddeev popov ghost fields is developed and applied to construct the brst extension of the off shell closed string amplitudes in the constant curvature gauge in this gauge the overlap path integral for off shell amplitudes is evaluated it leads to the nonlocal sewing procedure generating all off shell amplitudes from the cubic interaction vertex the general scheme of the reconstruction of a covariant closed string field theory from the off shell amplitudes is discussed within the path integral framework

periodic solutions of nonlinear boundary value problems one of the well known techniques in the theory of nonlinear boundary value problems bvp is the method of differential inequalities or the method of upper and lower solutions the method of alternative problems a global variant of the lyapunov schmidt method has been used in the study of problems at resonance the investigation of periodic bvp s forms an important subclass of problems at resonance our aim is to combine the two approaches to discuss nonlinear problems at resonance we restrict ourselves in this paper to the discussion of periodic boundary value problems in section 1 we shall indicate the method of upper and lower solutions the results for systems are given in a general way so as to include known results and also offer new directions section 2 deals with the abstract existence results at resonance in the desired framework in section 3 we consider the scalar periodic bvp s by combining the two techniques namely alternative methods and the method of differential inequalities

the weil petersson geodesic flow is ergodic we prove that the geodesic flow for the weil petersson metric on the moduli space of riemann surfaces is ergodic and in fact bernoulli and has finite positive metric entropy

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

the fenchel nielsen deformation the uniformization theorem provides that a riemann surface s of negative euler characteristic has a metric of constant curvature 1 a hyperbolic structure can be understood in terms of its deformations unfortunately the variation of the hyperbolic metric arising from a deformation is not determined by local data if z is a conformal coordinate for s and a ii h ii 00 1 a beltrami differential then dw dz p dj defines a new conformal coordinate and structure si the tensor p may vanish on the open set 0 c s and yet the hyperbolic metrics of s and si do not coincide on this phenomenon presents a s erious difficulty in the deformation theory of hyperbolic structures the fenchel nielsen twist deformation does not share this defect the deformation is defined by cutting the surface along a simple closed geodesic rotating one side of the cut relative to the other and attaching the sides in their new position a geodesic intersecting the cut is deformed to a broken geodesic the hyperbolic structure in the complement of the cut extends naturally to a hyperbolic structure on the new surface the deformation is concentrated at the cut the basic idea for the deformation appears in the work of fricke klein dehn and fenchel nielsen 71 8 in the fenchel nielsen manuscript the deformation was considered extensively coordinates for teichmiller space are defined in terms of the deformation the proper definition is given by a fuchsian group construction calculations are made in terms of unimodular matrices this approach is often cumbersome our basic objective is to give a description of the deformation in terms of quasiconformal mappings the bers embedding of teichmiiller space is central to the analytic theory of deformations using our characterization we calculate the first variation of the bers embedding for the fenchel nielsen deformation the result is a poincare series 6 which already appears in the work of petersson 16

closed geodesics periods and arithmetic of modular forms is the upper half plane and f is a discrete cocompact subgroup of sl 2 n acting by fractional linear transformations we demonstrate that in this case the periods over closed geodesics play a role somewhat similar to that of fourier coefficients of modular forms on sl 2 z and its congruence subgroups more specifically those periods uniquely determine a modular form theorem 2 this result is valid for cusp forms on any fuchsian group of the first kind with or without cusps and is closely related to the study of relative poincar6 series associated to closed geodesics for each integer k 2 and each closed geodesic 7o we define special cusp forms of weight 2k called relative poincar6 series ok t ol and prove that they generate the whole space s2k f of cusp forms theorem 1 in w 3 we give an expression for periods of a relative poincar6 series over closed geodesics in purely geometrical terms through the intersection of the corresponding geodesics theorem 3 an application of theorems 1 and 3 to arithmetic subgroups of sl 2 1r gives two natural rational structures o n s2k l n theorem 4 the relative poincar6 series have been studied for general f by petersson 18 19 and hejhal 5 g 2 wolpert 23 gives a basis of s4 f for g 2 for sl 2 tz the relative poincar6 series have been studied by zagier 25 kohnen 8 kohnen and zagier 9 and kramer 13 a related problem of constructing cusp forms of weight two associated to closed geodesics has been treated by kudla and millson in 143 in connection with the problem of

limits of geometrically tame kleinian groups let f be a finitely generated geometrically tame kleinian group with h3 f m when m has a finite volume the hyperbolic structure of m is unique up to homotopy by mostow s rigidity theorem but when m has infinite volume it is meaningful to consider the deformation space of the hyperbolic structure of m let ah m denote the space of faithful representations with discrete image from nl m to psl2 c modulo conjugacy with the topology of algebraic convergence until now only a little is known about ah m when f is of second kind there exists the space of quasi conformal deformation of f denoted by qho m with the quasi conformal or quasi isometric topology there is a canonical continuous injection t qho m ah m we abuse the notation qho m for t qho m the topological type of qho m has been determined by sullivan 21 one method for investigating ah m is to consider limits of sequences in qho m boundary groups in bers 3 and double limits in thurston 24 are such examples for considering limits it is important to determine when a sequence in ah m converges it was shown by thurston 24 and morgan shalen 16 that when m is acylindrical every sequence in ah m has a converging subsequence we gave in ohshika 19 a sufficient condition of convergence for geometrically finite groups in w 2 of this paper we prove a theorem which implies the existence of converging subsequence in all of the above cases the case of boundary groups double limits acylindrical manifolds and the theorem in 19 the statement is as follows

periodic boundary value problems for nonlinear higher order ordinary differential equations we study a class of boundary value problems for linear and nonlinear ordinary differential equations of higher order we study the solution set and present a maximum principle as a consequence we show the validity of the monotone method and obtain the extremal solutions between the upper and lower solutions

earthquakes on riemann surfaces and on measured geodesic laminations let s be a closed orientable surface of genus at least 2 we study properties of its techmuller space f s namely of the space of isotopy classes of conformal structures on s w p thurston introduced a certain compactification of f s by that he called the space of projective measured geodesic laminations he also introduced some transformations of teichmuller space called earthquakes which are intimately related to the geometry of f s a general problem is to understand which geometric properties of techmuller space subsist at infinity on thurston s boundarty in particular it is natural to ask whether earthquakes continuously extend at certain points of thurston s boundary and at precisely which points the do so this is the principal question addressed in this paper

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

solutions of two point bvps at resonance for higher order impulsive differential equations in this paper the resonance two point boundary value problems for impulsive 2n order differential equation x 2n t f t x t x t x 2n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 2n 1 k 1 p with following two point boundary value conditions x 2i 1 0 x 2i 1 1 i 0 n 1 and for n order differential equation x n t f t x t x t x n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 n 1 k 1 p with following periodic boundary value conditions x i 0 x i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the interest is that we allow the degree of variables of f to be greater than 1 the methods used and results obtained are new and they shows us that the solvability of these two problems are very much alike