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

multifactorial functions in fuzzy sets theory abstract the multifactorial function is a very important new concept which can be used to many aspects in fuzzy sets theory it appeared firstly in 5 where it was used to define fuzzy perturbation function and where the stability for the solutions of fuzzy relation equations by using fuzzy perturbation was studied in 6 by means of multifactorial functions multifactorial fuzzy sets and the multifactorial degree of nearness which are two new concepts too were given and they were used to multifactorial pattern recognition and clustering analysis with fuzzy characteristics in fact generally speaking most of the mathematical models dependent on several factors should use multifactorial functions especially fuzzy decision making fuzzy games fuzzy programming and fuzzy linear programming with several objective functions should here we study properties of multifactorial functions how to generate a new multifactorial function and we introduce in detail its applications in fuzzy pattern recognition fuzzy decision making fuzzy clustering fuzzy games and fuzzy programming etc

hyperbolic cone manifolds short geodesics and schwarzian derivatives given a geometrically finite hyperbolic cone manifold with the cone singularity sufficiently short we construct a one parameter family of cone manifolds decreasing the cone angle to zero we also control the geometry of this one parameter family via the schwarzian derivative of the projective boundary and the length of closed geodesics

classification of curvature collineations of plane symmetric static spacetimes a complete classification of curvature collineations of static plane symmetric spacetimes is obtained and then a comparison between isometries and ricci collineations of the corresponding metrics is given

classification of spherically symmetric static space times by their curvature collineations a complete classification of all spherically symmetric static space times according to their curvature collineations is presented and compared with ricci collineations of corresponding space times

regenerating singular hyperbolic structures from sol let m be a torus bundle over s 1 with an orientation preserving anosov monodromy the manifold m admits a geometric structure modeled on sol we prove that the sol structure can be deformed into singular hyperbolic cone structures whose singular locus m is the mapping torus of the fixed point of the monodromy the hyperbolic cone metrics are parametred by the cone angle in the interval 0 2 when 2 the cone manifolds collapse to the basis of the fibration s 1 and they can be rescaled in the direction of the fibers to converge to the sol manifold

the equivalence between fuzzy logic systems and feedforward neural networks demonstrates that fuzzy logic systems and feedforward neural networks are equivalent in essence first we introduce the concept of interpolation representations of fuzzy logic systems and several important conclusions we then define mathematical models for rectangular wave neural networks and nonlinear neural networks with this definition we prove that nonlinear neural networks can be represented by rectangular wave neural networks based on this result we prove the equivalence between fuzzy logic systems and feedforward neural networks this result provides us a very useful guideline when we perform theoretical research and applications on fuzzy logic systems neural networks or neuro fuzzy systems

laminations mesurees de plissage des varietes hyperboliques de dimension 3 for a hyperbolic metric on a 3 dimensional manifold the boundary of its convex core is a surface which is almost everywhere totally geodesic but which is bent along a family of disjoint geodesics the locus and intensity of this bending is described by a measured geodesic lamination which is a topological object we consider two problems the topological characterization of those measured geodesic laminations which can occur as bending measured laminations of hyperbolic metrics and the uniqueness problem which asks whether a hyperbolic metric is uniquely determined by its bending measured lamination

fixed points of compositions of earthquakes let s be a closed surface of genus at least 2 and consider two measured geodesic laminations that fill s right earthquakes along these laminations are diffeomorphisms of the teichmuller space of s we prove that the composition of these earthquakes has a fixed point in the teichmuller space another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic ads manifold the proof uses some estimates from the geometry of those ads manifolds

dehn filling volume and the jones polynomial given a hyperbolic 3 manifold with torus boundary we bound the change in volume under a dehn filling where all slopes have length at least 2 this result is applied to give explicit diagrammatic bounds on the volumes of many knots and links as well as their dehn fillings and branched covers finally we use this result to bound the volumes of knots in terms of the coefficients of their jones polynomials

lower bounds on volumes of hyperbolic haken 3 manifolds we prove a volume inequality for 3 manifolds having c o metrics bent along a surface and satisfying certain curvature conditions the result makes use of perelman s work on the ricci flow and geometrization of closed 3 manifolds corollaries include a new proof of a conjecture of bonahon about volumes of convex cores of kleinian groups improved volume estimates for certain haken hyperbolic 3 manifolds and a lower bound on the minimal volume of orientable hyperbolic 3 manifolds an appendix compares estimates of volumes of hyperbolic 3 manifolds drilled along a closed embedded geodesic with experimental data

projective structures with degenerate holonomy and the bers density conjecture we prove the bers density conjecture for singly degenerate kleinian surface groups without parabolics

extended neuro fuzzy models of multilayer perceptrons in this paper the famous neural model the multilayer perceptron is extended to a new neural model that is called the additive takagi sugeno type multilayer perceptron the present study proves that this new model can also act as a universal approximator and thus it can be used in many fields such as system modeling and identification the concept of f duality and the fuzzy operator interactive or are used to prove that the proposed neural model is functionally equal to a kind of fuzzy inference system further this paper presents another new neuro fuzzy model that is called the sigmoid adaptive network based fuzzy inference system simulation studies show that our proposed models both have stronger approximation capability than multilayer perceptrons

pinching constants for hyperbolic manifolds we show in this paper that for everyn 4 there exists a closedn dimensional manifoldv which carries a riemannian metric with negative sectional curvaturek but which admits no metric with constant curvaturek 1 we also estimate the pinching constantsh for which our manifoldsv admit metrics with 1 k h

a genetic based neuro fuzzy approach for modeling and control of dynamical systems linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems and fuzzy logic represents one of the most effective algorithms to build such linguistic models in this paper a linguistic qualitative modeling approach is proposed the approach combines the merits of the fuzzy logic theory neural networks and genetic algorithms gas the proposed model is presented in a fuzzy neural network fnn form which can handle both quantitative numerical and qualitative linguistic knowledge the learning algorithm of a fnn is composed of three phases the first phase is used to find the initial membership functions of the fuzzy model in the second phase a new algorithm is developed and used to extract the linguistic fuzzy rules in the third phase a multiresolutional dynamic genetic algorithm mrd ga is proposed and used for optimized tuning of membership functions of the proposed model two well known benchmarks are used to evaluate the performance of the proposed modeling approach and compare it with other modeling approaches

variable universe stable adaptive fuzzy control of a nonlinear system abstract a kind of stable adaptive fuzzy control of a nonlinear system is implemented based on the variable universe method proposed first in 1 first of all the basic structure of variable universe adaptive fuzzy controllers is briefly introduced then the contraction expansion factor which is a key tool of the variable universe method is defined by means of the integral regulation idea and then a kind of adaptive fuzzy controller is designed by using such a contraction expansion factor the simulation on the first order nonlinear system is done and as a result its simulation effect is quite good in comparison with the corresponding result in 2 3 second it is proved that the variable universe adaptive fuzzy control is asymptotically stable by use of liapunov theory the simulation on a second order nonlinear system shows that its simulation effect is also quite good in comparison with the corresponding result in 2 besides a useful tool called symbolic factor is proposed which may be of universal significance it can greatly reduce the setting time and enhance the robustness of the system

equivalences between neural autoregressive time series models and fuzzy systems soft computing sc emerged as an integrating framework for a number of techniques that could complement one another quite well artificial neural networks fuzzy systems evolutionary algorithms probabilistic reasoning since its inception a distinctive goal has been to dig out the deep relationships among their components this paper considers two wide families of sc models on the one hand the regime switching autoregressive paradigm is a recent development in statistical time series modeling and it includes a set of models closely related to artificial neural networks on the other hand we consider fuzzy rule based systems in the framework of time series analysis this paper discloses original results establishing functional equivalences between models of these two classes and hence opens the door to a productive line of research where results and techniques from one area can be applied in the other as a consequence of the equivalences presented in this paper we prove the asymptotic stationarity of a class of fuzzy rule based systems simulations based on information criteria show the importance of the selection of the proper membership function

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

generalized single hidden layer feedforward networks for regression problems in this paper traditional single hidden layer feedforward network slfn is extended to novel generalized slfn gslfn by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes the significant contributions of this paper are as follows 1 a primal gslfn p gslfn is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated 2 a simplified gslfn s gslfn is realized by decomposing the polynomial output weights of the p gslfn into randomly generated polynomial nodes and tunable output weights 3 both p and s gslfn are able to achieve universal approximation if the output weights are tuned by ridge regression estimators and 4 by virtue of the developed batch and online sequential ridge elm br elm and osr elm learning algorithms high performance of the proposed gslfns in terms of generalization and learning speed is guaranteed comprehensive simulation studies and comparisons with standard slfns are carried out on real world regression benchmark data sets simulation results demonstrate that the innovative gslfns using br elm and osr elm are superior to standard slfns in terms of accuracy training speed and structure compactness

functional equivalence between radial basis function networks and fuzzy inference systems it is shown that under some minor restrictions the functional behavior of radial basis function networks rbfns and that of fuzzy inference systems are actually equivalent this functional equivalence makes it possible to apply what has been discovered learning rule representational power etc for one of the models to the other and vice versa it is of interest to observe that two models stemming from different origins turn out to be functionally equivalent

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

application of hybrid system control method for real time power system stabilization the electrical energy has become the major form of energy for end use consumption in today s world there is always a need of making electric energy generation more economic and reliable for proper operation this large integrated system requires a stable operating condition the power system is a dynamic system it is constantly being subjected to small disturbances which cause the generators relative angles to change a r messina et al an investigation on the use of power system stabilizers for damping inter area oscillations in longitudinal power systems ieee trans power systems 13 2 1997 for the interconnected system to be able to supply the load power demand when the transients caused by disturbance die out a new acceptable steady state operating condition is reached a soos an optimal adaptive power system stabilizer ph d thesis university of calgary october 1997 it is important that these disturbances do not drive the system to an unstable condition the small signal stability problem is associated with modes of oscillations affecting either a single machine local modes or a small group of relatively closely connected machines or inter area global modes this problem has got a very high attention in the last three decades and many types of controllers depend on classical and modern control theory have been developed by designing supplementary control signals to improve system damping a r messina et al an investigation on the use of power system stabilizers for damping inter area oscillations in longitudinal power systems ieee trans power systems 13 2 1997 in this research a novel power system stabilizer for damping both local and global modes of an interconnected system based on neuro fuzzy hybrid system is developed nn miso neural network multiple input single output is proposed for local modes and takagi sugneo s neuro fuzzy system is proposed for global modes control a soos an optimal adaptive power system stabilizer ph d thesis university of calgary october 1997 a comparative study between the proposed controller and most of widely used types of controllers i e optimal controller and lead lag stabilizer are made towards damping electromechanical modes of oscillations the results proved the potency of hybrid controller for power system stability control d chakraborty n r pal integrated feature analysis and fuzzy rule based system identification in a neuro fuzzy paradigm ieee trans systems man cybernet 31 3 2001 391 400

collisions of particles in locally ads spacetimes i local description and global examples we investigate 3 dimensional globally hyperbolic ads manifolds or more generally constant curvature lorentz manifolds containing particles i e cone singularities along a graph we impose physically relevant conditions on the cone singularities e g positivity of mass angle less than 2 on time like singular segments we construct examples of such manifolds describe the cone singularities that can arise and the way they can interact the local geometry near the vertices of we then adapt to this setting some notions like global hyperbolicity which are natural for lorentz manifolds and construct some examples of globally hyperbolic ads manifolds with interacting particles

collineations of the ricci tensor ricci collineations for the ricci tensor which is constructed from a general spherically symmetric and static metric are classified for all possibilities of rab r such that rab 0 for a b it turns out that the only collineations admitted by this tensor can be ten six or four and there does not appear any case in between

quasi fuchsian manifolds with particles we consider 3 dimensional hyperbolic cone manifolds which are convex cocompact in a natural sense with cone singularities along infinite lines such singularities are sometimes used by physicists as models for massive spinless point particles we prove an infinitesimal rigidity statement when the angles around the singular lines are less than any infinitesimal deformation changes either these angles or the conformal structure at infinity with marked points corresponding to the endpoints of the singular lines moreover any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone manifold structure these results hold also when the singularities are along a graph i e for interacting particles

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

cusp shapes under cone deformation a horospherical torus about a cusp of a hyperbolic manifold inherits a euclidean similarity structure called a cusp shape we bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp the bounds are in terms of the change in structure in a neighborhood of the singular locus alone we then apply this result to provide information on the cusp shape of many hyperbolic knots given only a diagram of the knot specifically we show there is a universal constant c such that if a knot admits a prime twist reduced diagram with at least c crossings per twist region then the length of the second shortest curve on the cusp torus is bounded the bound is linear in the number of twist regions of the diagram

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties

examples of relative deformation spaces that are not locally connected we provide an infinite family of pared manifolds with the property that the relative deformation spaces of hyperbolic structures on these manifolds are not locally connected this is a natural extension of the recent result of bromberg that shows the space of kleinian punctured torus groups is not locally connected