dehn surgery on arborescent links this paper studies dehn surgery on a large class of links called arborescent links it will be shown that if an arborescent link l is sufficiently complicated in the sense that it is composed of at least 4 rational tangles t pl qi with all qj 2 and none of its length 2 tangles are of the form t 1 2ql 1 2q2 then all complete surgeries on l produce haken manifolds the proof needs some result on surgery on knots in tangle spaces let t r 2s p 2q b ti u t2 li k be a tangle with k a closed circle and let m b int n ti u t2 we will show that if s 1 and p 1 mod 2q then om remains incompressible after all nontrivial surgeries oln k two bridge links are a subclass of arborescent links for such a link l p q most dehn surgeries on it are non haken however it will be shown that all complete surgeries yield manifolds containing essential laminations unless p q has a partial fraction decomposition of the form 1 r 1 s in which case it does admit non laminar surgeries

cusp geometry of fibered 3 manifolds let f be a surface and suppose that varphi colon f to f is a pseudo anosov homeomorphism fixing a puncture p of f the mapping torus m m varphi is hyperbolic and contains a maximal cusp c about the puncture p we show that the area and height of the cusp torus partial c is equal to the stable translation distance of varphi acting on the arc complex scr a f p up to an explicitly bounded multiplicative error our proof relies on elementary facts about the hyperbolic geometry of pleated surfaces in particular the proof of this theorem does not use any deep results from teichm uller theory kleinian group theory or the coarse geometry of scr a f p a similar result holds for quasi fuchsian manifolds n cong f times bbb r in that setting we find a combinatorial estimate for the area and height of the cusp annulus in the convex core of n up to explicitly bounded multiplicative and additive error as an application we show that covers of punctured surfaces induce quasi isometric embeddings of arc complexes

deformations of representations of discrete subgroups of so 3 1 certainly the case of manifolds is the most interesting and most complicated the main aim of this paper is to show that conjecture i is not absolutely groundless first our results deal with reflection orbifolds in this case we will prove conjecture 1 and find that r tq m 4 is a smooth manifold of dimension f 4 where f is the number of faces of the reflection orbifold theorem 1 then we shall consider orbifolds of finite volume and examine the restriction map

right l groups geometric garside groups and solutions of the quantum yang baxter equation abstract right lattice ordered groups are introduced and studied as a general framework for garside groups and related groups without a garside element every right l group g has a two sided partially ordered subgroup n g which generalizes the quasi centre of an artin tits group the group n g splits into copies of z if g is noetherian the positive cone of a right l group is described as a structure that is known from algebraic logic a pair of left and right self similar hoops for noetherian right l groups g modularity of the lattice structure is characterized in terms of an operation on the set x g of atoms it is proved that modular garside groups are equivalent to finite projective spaces with a non degenerate labelling a concept of duality for x g is introduced and applied in the distributive case this gives a one to one correspondence between noetherian right l groups with duality and non degenerate unitary set theoretic solutions of the quantum yang baxter equation the description of garside groups via garside germs is extended to right l groups which yields a one sided enhancement and a new proof of dvurecenskij s non commutative extension of mundici s correspondence between abelian l groups and mv algebras

dynamic response of non linear systems to poisson distributed random impulses abstract the dynamic response of non linear systems to external excitations in form of a poisson distributed train of random impulses is considered the state vector of the dynamical system under consideration is a poisson driven markov vector process the equations governing its joint statistical moments are obtained by making use of a generalized ito s differential rule the resulting infinite hierarchy of equations is truncated with the help of a cumulant neglect closure of different orders for a duffing oscillator the time histories of the mean value the variance and the skewness coefficient of the response are evaluated analytically and compared with those obtained from monte carlo simulations it is found that if the departure of the poisson driven excitation process from gaussianity ranges from small to moderately large i e the expected arrival rate of impulses is not very low the application of the fourth order cumulant neglect closure technique i e neglecting the cumulants above the fourth order yields very good estimates of the response mean values and variances

response of nonlinear systems in probability domain using stochastic averaging determination of probability density function pdf of the response for strongly nonlinear single degree of freedom system subjected to both multiplicative and additive random excitations using stochastic averaging technique is faced with few difficulties firstly the size of excitations should be small such that the response of the system converges weakly to a markov process secondly the excitations should preferably be broad banded so that the analytical results are reasonably accurate and finally the nonlinear functions should be integrable if closed formed expressions for the result are desired the above issues are examined in the paper with a view to show a limiting values of the size parameter of excitations for which stochastic averaging technique can be applied to obtain reasonable estimates of pdf and mean square value of response b the effect of the nature of the frequency contents of excitation on the response and c the use of the stochastic averaging method employing generalized harmonic functions for nonintegrable functions representing the dynamic system it is shown that the stochastic averaging procedure provides results which compare very well with those obtained from simulation analysis not only for wide band excitations but also for narrow band excitations for a wide range of the size parameter of excitation further the procedure can be easily implemented for highly irregular functions by employing a numerical scheme with fft

self similarity in diffraction by a self similar fractal screen using the sierpinski gasket as an example it has been shown here that the paraxial fraunhoffer zone diffracted field of a self similar fractal screen also exhibits self similarity this also establishes that fractal structures can be used with great profit in problems involving array syntheses recently it has been shown that the sierpinski gasket is itself a member of a much wider class of gaskets and the potential for the use of fractal structures in electromagnetic em problems may be vast indeed

foliations orders representations l spaces and graph manifolds abstract we show that the properties of admitting a co oriented taut foliation and having a left orderable fundamental group are equivalent for rational homology 3 sphere graph manifolds and relate them to the property of not being a heegaard floer l space this is accomplished in several steps first we show how to detect families of slopes on the boundary of a seifert fibred manifold in four different fashions using representations using left orders using foliations and using heegaard floer homology then we show that each method of detection determines the same family of detected slopes next we provide necessary and sufficient conditions for the existence of a co oriented taut foliation on a graph manifold rational homology 3 sphere respectively a left order on its fundamental group which depend solely on families of detected slopes on the boundaries of its pieces the fact that heegaard floer methods can be used to detect families of slopes on the boundary of a seifert fibred manifold combines with certain conjectures in the literature to suggest an l space gluing theorem for rational homology 3 sphere graph manifolds as well as other interesting problems in heegaard floer theory

quasigeodesic pseudo anosov flows in hyperbolic 3 manifolds and connections with large scale geometry abstract in this article we obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo anosov flow in a closed hyperbolic three manifold to be quasigeodesic quasigeodesic means that orbits are efficient in measuring length up to a bounded multiplicative distortion when lifted to the universal cover we prove that such flows are quasigeodesic if and only if there is an upper bound depending only on the flow on the number of orbits which are freely homotopic to an arbitrary closed orbit of the flow the main ingredient is a proof that under the boundedness condition the fundamental group of the manifold acts as a uniform convergence group on a flow ideal boundary of the universal cover we also construct a flow ideal compactification of the universal cover and prove that it is equivariantly homeomorphic to the gromov compactification this implies the quasigeodesic behavior of the flow the flow ideal boundary and flow ideal compactification are constructed using only the structure of the flow

statistical linearization of the duffing oscillator under non gaussian external excitation the duffing oscillator under external non gaussian excitations is investigated by means of statistical linearization the input process is modelled as a polynomial of a gaussian process or as a renewal driven impulse process four criteria of statistical linearization are considered the interarrival times of the renewal process are distributed according to a pearson type iii law predictions of the stationary variance are compared with monte carlo simulations

response of stochastic dynamical systems driven by additive gaussian and poisson white noise solution of a forward generalized kolmogorov equation by a spectral finite difference method abstract a numerical method is given for the solution of the probability density function of the response process of memoryless one and two state dynamical systems having polynomial restoring forces and which are subjected to a combination of gaussian and poisson white noises the method employs the fourier transformed forward generalized kolmogorov equation to arrive at an initial boundary value problem for the characteristic function which is solved using a high order finite difference procedure the probability density function is recovered by numerical inverse fourier transformation several examples are given the results of which are compared with analytical solutions where available and with simulation otherwise

cosmetic surgery in l spaces and nugatory crossings the cosmetic crossing conjecture also known as the nugatory crossing conjecture asserts that the only crossing changes that preserve the oriented isotopy class of a knot in the 3 sphere are nugatory we use the dehn surgery characterization of the unknot to prove this conjecture for knots in integer homology spheres whose branched double covers are l spaces satisfying a homological condition this includes as a special case all alternating and quasi alternating knots with square free determinant as an application we prove the cosmetic crossing conjecture holds for all knots with at most nine crossings and provide new examples of knots including pretzel knots non arborescent knots and symmetric unions for which the conjecture holds

numerical meshfree path integration method for non linear dynamic systems abstract we present a new numerical meshfree path integration mpi method for non linear dynamic systems the obtained mpi method can be performed in the irregular computational domain and the probability density values of the random nodes in the domain can be calculated via the mpi method and the ordinary differential equations for the first and second order moments on the basis of gaussian closure method the piecewise linear interpolation based on adaptive least squares is utilized as a post processor to approximate the probability density values on arbitrary positions the good performance of the resulting method is finally shown in the numerical examples by using three specific non linear dynamic systems duffing oscillator subjected to both harmonic and stochastic excitations duffing rayleigh oscillator subjected to both harmonic and stochastic excitations and chen system driven by three different gaussian white noises

exact stationary probability density for second order non linear systems under external white noise excitation abstract in this paper exact stationary solutions are constructed for non linear dynamical systems subjected to stochastic excitation the solution of the equations 6 7 in this paper is demonstrated to be unique and then the results of references 10 11 are shown to be generalized therefore new exact stationary solutions that satisfies the fokker plank kolmogorov fpk equation is obtainable

fractal sequences derived from the self similar extensions of the sierpinski gasket the well known sierpinski gasket has been generalised by the authors into the generalised pascal sierpinski gaskets gpsg of orders k l where both k and l are or 2 it has been shown here that families of self similar sequences can be derived from these extensions of the sierpinski gasket when k 2 and l is a prime number

laminations and groups of homeomorphisms of the circle if m is an atoroidal 3 manifold with a taut foliation thurston showed that 1 m acts on a circle here we show that some other classes of essential laminations also give rise to actions on circles in particular we show this for tight essential laminations with solid torus guts we also show that pseudo anosov flows induce actions on circles in all cases these actions can be made into faithful ones so 1 m is isomorphic to a subgroup of homeo s1 in addition we show that the fundamental group of the weeks manifold has no faithful action on s1 as a corollary the weeks manifold does not admit a tight essential lamination with solid torus guts a pseudo anosov flow or a taut foliation finally we give a proof of thurston s universal circle theorem for taut foliations based on a new purely topological proof of the leaf pocket theorem

on definite strongly quasipositive links and l space branched covers abstract we investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised seifert forms and apply our results to the problem of determining when such a link can have an l space cyclic branched cover in particular we show that if n 1 2 n 1 is the dual garside element and b n k p b n is a strongly quasipositive braid whose braid closure b is definite then k 2 implies that b is one of the torus links t 2 q t 3 4 t 3 5 or pretzel links p 2 2 m p 2 3 4 applying 7 theorem 1 1 we deduce that if one of the standard cyclic branched covers of b is an l space then b is one of these links we show by example that there are strongly quasipositive braids n p whose closures are definite but not one of these torus or pretzel links we also determine the family of definite strongly quasipositive 3 braids and show that their closures coincide with the family of strongly quasipositive 3 braids with an l space branched cover

links of rational singularities l spaces and lo fundamental groups we prove that the link of a complex normal surface singularity is an l space if and only if the singularity is rational this via a result of hanselman et al taut foliations on graph manifolds 2015 arxiv 1508 0591 proving the conjecture of boyer et al math ann 356 4 1213 1245 2013 shows that a singularity link is not rational if and only if its fundamental group is left orderable if and only if it admits a coorientable taut foliation

on the spatial fourier transforms of the pascal sierpinski gaskets it has been shown here that the fourier transform which can be obtained experimentally of an evolving fractal can be manipulated to yield the fractal dimension although only the pascal sierpinski gaskets have been considered here because of their generality it is expected that this technique can be utilized to identify other planar fractals as well

holomorphic disks and three manifold invariants properties and applications in 27 we introduced floer homology theories hf y s hf y s hf y t hf y s and hf red y s associated to closed oriented three manifolds y equipped with a spiny structures s spin c y in the present paper we give calculations and study the properties of these invariants the calculations suggest a conjectured relationship with seiberg witten theory the properties include a relationship between the euler characteristics of hf and turaev s torsion a relationship with the minimal genus problem thurston norm and surgery exact sequences we also include some applications of these techniques to three manifold topology

incompressibility criteria for spun normal surfaces we give a simple sufficient condition for a spun normal surface in an ideal triangulation to be incompressible namely that it is a vertex surface with non empty boundary which has a quadrilateral in each tetrahedron while this condition is far from being necessary it is powerful enough to give two new results the existence of alternating knots with non integer boundary slopes and a proof of the slope conjecture for a large class of 2 fusion knots

probabilistic solution of nonlinear oscillators excited by combined gaussian and poisson white noises abstract the stationary probability density function pdf solution of the stochastic response of nonlinear oscillators is investigated in this paper the external excitation is assumed to be a combination of gaussian and poisson white noises the pdf solution is governed by the generalized kolmogorov equation which is solved by the exponential polynomial closure epc method in order to evaluate the effectiveness of the epc method different nonlinear oscillators are considered in numerical analysis nonlinearity exists either in displacement or in velocity for these nonlinear oscillators the impulse arrival rate mono modal pdf and bi modal pdf are also considered in this study compared to the pdf given by monte carlo simulation the epc method presents good agreement with the simulated result which can also be observed in the tail region of the pdf solution

commensurability of 1 cusped hyperbolic 3 manifolds we give examples of non fibered hyperbolic knot complements in homology spheres that are not commensurable to fibered knot complements in homology spheres in fact we give many examples of knot complements in homology spheres where every commensurable knot complement in a homology sphere has non monic alexander polynomial

response of dynamic systems to poisson white noise abstract a method is developed for finding response statistics and reliability for a non linear system subjected to poisson white noise the poisson white noise can be viewed as a sequence of independent indentically distributed pulses arriving in time according to a poisson counting process the method is based on the observation that the system experiences free vibrations between consecutive pulses of the input two algorithms are used for analysis the first uses the definition of the poisson white noise and the second is based on an approximate representation of the poisson white noise referred to as binomial white noise the binomial white noise is an independent time series with a fixed time step that can be zero with a finite probability the time step of the first and second algorithms are random and deterministic respectively the algorithms are used to calculate transition probabilities and estimate response statistics numerical examples are presented to demonstrate the proposed method of response and reliability analysis

on l spaces and left orderable fundamental groups examples suggest that there is a correspondence between l spaces and three manifolds whose fundamental groups cannot be left ordered in this paper we establish the equivalence of these conditions for several large classes of manifolds in particular we prove that they are equivalent for any closed connected orientable geometric three manifold that is non hyperbolic a family which includes all closed connected orientable seifert fibred spaces we also show that they are equivalent for the twofold branched covers of non split alternating links to do this we prove that the fundamental group of the twofold branched cover of an alternating link is left orderable if and only if it is a trivial link with two or more components we also show that this places strong restrictions on the representations of the fundamental group of an alternating knot complement with values in text homeo s 1

non standard components of the character variety for a family of montesinos knots we show that there are montesinos knots with n 1 geq 4 tangles whose character varieties contain arbitrarily many irreducible components of dimension d for any 1 le d le n 2 moreover these irreducible components can be chosen so that the trace of the meridian is non constant

on a new class of planar fractals the pascal sierpinski gaskets a new class of planar fractals called the pascal sierpinski gaskets is described of which the well known sierpinski gasket is a special case some of these gaskets are true mandelbrot fractals possessing non integral dimensions as well as self similarity the remaining ones are not self similar but appear to have nonintegral dimensions

on character varieties sets of discrete characters and nonzero degree maps a it knot manifold is a compact connected irreducible orientable 3 manifold whose boundary is an incompressible torus we first investigate virtual epimorphisms between the fundamental groups of small knot manifolds and prove minimality results for small knot manifolds with respect to nonzero degree maps these results are applied later in the paper where we fix a small knot manifold m and investigate various sets of characters of representations rho pi 1 m to rm psl 2 bbb c whose images are discrete we show that the topology of these sets is intimately related to the algebraic structure of the rm psl 2 bbb c character variety of m as well as dominations of manifolds by m and its dehn fillings we apply our results to the following question of shicheng wang it are nonzero degree maps between infinitely many distinct dehn fillings of two hyperbolic knot manifolds m and n induced by a nonzero degree map m to n we show that the answer is yes generically using this we show that if a small mathcal h minimal hyperbolic knot manifold admits non homeomorphic mathcal h minimal dehn fillings it admits infinitely many such fillings we also construct the first infinite families of small closed connected orientable manifolds which are minimal in the sense that they do not admit nonzero degree maps other than homotopy equivalences to any aspherical manifold

local averaged path integration method approach for nonlinear dynamic systems abstract traditional path integration method always has a limited time step length whose minimum is based on the subdivision degree of integral space in order to numerically analyze a smaller time step probability evolution without significant increase in computing time a new local averaged path integration lapi method is investigated the basic idea of this method is giving a local averaged value of transition probability density function tpdf then the numerical integration of chapman kolmogorov ck equation to the local averaged probability density function pdf will be calculated in lower space subdivision degree second order partial derivative of pdf can be used to correct the deviation between local averaged pdf and the real one it is demonstrated that the proposed method can give a more efficient calculation compared with traditional gauss legendre path integration glpi in the case of our method smaller time step value is permitted with the same space subdivision degree and smaller space subdivision degree is needed to keep the accuracy of stationary pdf with the same time step value this merits also exist when analyzing transient pdf which leads to a better capability of capturing the evolution of the pdf

floer simple manifolds and l space intervals abstract an oriented three manifold with torus boundary admits either no l space dehn filling a unique l space filling or an interval of l space fillings in the latter case which we call floer simple we construct an invariant which computes the interval of l space filling slopes from the turaev torsion and a given slope from the interval s interior as applications we give a new proof of the classification of seifert fibered l spaces over s 2 and prove a special case of a conjecture of boyer and clay 6 about l spaces formed by gluing three manifolds along a torus

exceptional and cosmetic surgeries on knots we show that the bridge distance of a knot determines a lower bound on the genera of essential surfaces and heegaard surfaces in the manifolds that result from non trivial dehn surgeries on the knot in particular knots with high bridge distance do not admit non trivial non hyperbolic surgeries or non trivial cosmetic surgeries we further show that if a knot has bridge distance at least 3 then its bridge number is bounded above by a function of seifert genus or indeed by the genus of almost any essential surface or heegaard surface in the surgered manifold

maximum entropy principle and nonlinear stochastic oscillators abstract the principle of maximum entropy introduced first in physics and successfully applied in many other fields e g statistics reliability estimation simulation has recently been developed to analyze the systems governed by stochastic differential equations in this paper we extend the maximum entropy method to the general class of stochastic nonlinear systems and apply it to stochastic nonlinear oscillators to indicate the effectiveness of the method a comparison of the results with predictions of the known procedures is shown graphically the analysis presented in this paper indicates that the maximum entropy principle can serve as a general method for determining the probability distributions of a wide class of stochastic systems when we have only a partial information in the form of moments or equations for moments

computing boundary slopes of 2 bridge links we describe an algorithm for computing boundary slopes of 2bridge links as an example we work out the slopes of the links obtained by 1 k surgery on one component of the borromean rings a table of all boundary slopes of all 2 bridge links with 10 or less crossings is also included

stochastic response of a ϕ6 oscillator subjected to combined harmonic and poisson white noise excitations abstract the transient and stationary probability density functions pdfs of stochastic response of the 6 duffing oscillator under combined harmonic and external and parametric poisson white noises excitations are investigated by the generalized cell mapping method in this paper based on the digraph analysis method the global qualitative properties are obtained such as attractors basins of attraction basin boundaries saddles and invariant manifolds the evolutionary process of transient and stationary pdfs are shown based on the matrix analysis method it is observed that there is a close relationship between evolutionary direction of pdf and the unstable manifold monte carlo mc simulation is used to verify the accuracy of the matrix analysis method

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

the ring of k regular sequences ii in this paper we continue our study of k regular sequences begun in 1992 we prove some new results give many new examples from the literature and state some open problems

immersed surfaces and seifert fibered surgery on montesinos knots we will use immersed surfaces to study seifert fibered surgery on montesinos knots and show that if 1 q1 1 1 q2 1 1 q3 1 1 then a montesinos knot k p q1 p2 q2 p3 q3 admits no atoroidal seifert fibered surgery

on the set of l space surgeries for links abstract we study the qualitative structure of the set ls of integral l space surgery slopes for links with two components it is known that the set of l space surgery slopes for a nontrivial l space knot is always a positive half line however already for two component torus links the set ls has a very complicated structure e g in some cases it can be unbounded from below in order to probe the geometry of this set we ask if it is bounded from below for more general l space links with two components for algebraic two component links we provide three complete characterizations for the boundedness from below one in terms of the alexander polynomial one in terms of the embedded resolution graph and one in terms of the so called h function introduced by the authors in 9 it turns out that ls is bounded from below for most algebraic links if it is unbounded from below it must contain a negative half line parallel to one of the axes we also give a sufficient condition for boundedness for arbitrary l space links

generalized sierpinski fractal multiband antenna a new set of fractal multiband antennas called mod p sierpinski gaskets is presented mod p sierpinski fractal antennas derive from the pascal triangle and present a log periodic behavior which is a consequence of their self similarity properties mod p sierpinski fractal antennas constitute a generalization of the classical sierpinski antenna

holomorphic disks and knot invariants abstract we define a floer homology invariant for knots in an oriented three manifold closely related to the heegaard floer homologies for three manifolds defined in an earlier paper we set up basic properties of these invariants including an euler characteristic calculation and a description of the behavior under connected sums then we establish a relationship with hf for surgeries along the knot applications include calculation of hf of three manifolds obtained by surgeries on some special knots in s 3 and also calculation of hf for certain simple three manifolds which fiber over the circle

minimal index torsion free subgroups of kleinian groups a kleinian group is a discrete subgroup of psl 2 c the full group of orientation preserving isometries of 3 dimensional hyperbolic space in the language of t1 q h3 is a hyperbolic 3 orbifold that is a metric 3 orbifold in which all sectional curvatures are 1 and for which is the orbifold fundamental group see t1 for further details a fuchsian group is a discrete subgroup of psl 2 r and as such acts discontinuously on the hyperbolic plane we define to be of finite co volume resp co area if the volume resp area of the quotient orbifold q is finite by selberg s lemma if is a kleinian resp fuchsian group of finite covolume resp co area it contains a torsion free subgroup of finite index by definition any torsion free subgroup cannot contain any finite subgroups of so the index must be a multiple of the lowest common multiple of all orders of finite subgroups of see cfjr for a proof being of finite co volume implies there are only finitely many conjugacy classes of finite subgroups thus we make the following

extreme value prediction for non linear stochastic oscillators via numerical solutions of the stationary fpk equation abstract the accuracy of two well established numerical methods is demonstrated and the importance of bandwidth examined for computationally efficient markov based extreme value predictions associated with finite duration stationary sample paths of a non linear oscillator driven by gaussian white noise by making the poisson assumption of independent upcrossings extreme exceedance probabilities are predicted via the mean threshold crossing rate using numerical solutions of the stationary fokker planck fpk equation with bandwidth initially ignored predicted exceedances using the weighted residual methods of bhandari and sherrer soize and kunert and the finite element method of langley are compared with nominally exact predictions for a heavily damped duffing type model obtained by using an explicit fpk solution the fe method being established as superior predictions via fe solutions are then compared with very long monte carlo simulations in which bandwidth effects are included two lightly damped non linear oscillator models are examined both with cubic stiffness but different damping mechanisms one model again being of simple duffing type with linear damping the other being appropriate to single co ordinate random vibration of a clamped clamped beam with wholly non linear damping the realistic damping parameter values assigned to the beam model are statistically equivalent to the linear damping level chosen for the simple model at just above 1 at this overall damping level results clearly demonstrate that for the probability levels and durations considered bandwidth is only important for the linearly damped model for the beam model with non linear damping bandwidth can be ignored allowing accurate extreme exceedance predictions by using only the stationary fpk equation the paper also demonstrates that the limiting decay rate of the first passage probability advocated by crandall roberts and others as a criterion for deciding the barrier height above which first passage times can be assumed independent proves grossly over conservative as a corresponding criterion for deciding the independence level for use in stationary extreme value prediction

fractal structures derivable from the generalisations of the pascal triangle generalisations of order k or 2 of the pascal triangle are used to construct generalised pascal sierpinski gaskets of orders k l or 2 it is shown that all such gaskets are self affine fractals but when k 2 and l is prime then the gasket is rigorously self similar and possesses a similarity dimension the evolutionary morphology of the gaskets of orders k l prime bears a resemblance to the growth of pyrolitic graphite films and other material structures

stochastic stationary response of a variable mass system with mass disturbance described by poisson white noise abstract variable mass systems have received widespread attention and show prominent significance with the explosive development of micro and nanotechnologies so there is a growing need to study the influences of mass disturbances on systems this paper is devoted to investigating the stochastic response of a variable mass system subject to weakly random excitation in which the mass disturbance is modeled as a poisson white noise firstly the original system is approximately replaced by the associated conservative system with small disturbance based on the taylor expansion technique then the stationary response of the approximate system is obtained by applying the stochastic averaging method at last a representative variable mass oscillator is worked out to illustrate the effectiveness of the analytical solution by comparing with monte carlo simulation the relative change of mean square displacement is used to measure the influences of mass disturbance on system responses results reveal that the stochastic responses are more sensitive to mass disturbance for some system parameters it is also found that the influences of poisson white noise as the mass disturbance on system responses are significantly different from that of gaussian white noise of the same intensity

cyclic surgery degrees of maps of character curves and volume rigidity for hyperbolic manifolds this paper proves a theorem about dehn surgery using a new theorem about psl2c character varieties confirming a conjecture of boyer and zhang this p aper shows that a small hyperbolic knot in a homotopy sphere having a non trivial cyclic slope r has an incompressible surface with non integer boundary slope strictly between r 1 and r 1 a corollary is that any small knot which has only integer boundary slopes has property p the proof uses connections between the topology of the complement of the knot m and the psl2c character variety of m that were discovered by culler and shalen the key lemma which should be of independent interest is that for certain components of the character variety of m the map on character varieties induced by m m is a birational isomorphism onto its image this in turn depends on a fancy version of mostow rigidity due to gromov thurston and goldman the proof of the theorem about dehn surgery also gives information about the diameter of the set of boundary slopes of m let me start with the theorem about dehn surgery let k be a knot in a compact closed 3manifold that is a tame embedding s 1 the complement of k m is minus an open regular neighborhood of k so m is a compact 3 manifold whose boundary is a torus suppose is a simple closed curve in m we can create a closed manifold m from m by taking a solid torus and gluing its boundary to m in such a way that bounds a disc in the solid torus m depends only on the isotopy class of the new manifold m is called a dehn filling of m or a dehn surgeryon k recently many people have studied what kinds of manifolds arise when you

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

bundles and finite foliations by a hyperbolic manifold we shall always mean a complete orientable hyperbolic manifold of nite volume we recall that if is a kleinian group then it is said to be geometrically nite if there is a nite sided convex fundamental domain for the action of on hyperbolic space otherwise is geometrically in nite if happens to be a surface group then we say it is quasi fuchsian if the limit set for the group action is a jordan curve c and preserves the components of s n c the starting point for this work is the following theorem which is a combination of theorems due to marden thurston and bonahon

dehn fillings of large hyperbolic 3 manifolds let m be a compact connected orientable hyperbolic 3 manifold whose boundary is a torus and which contains an essential closed surface s i t is conjectured that 5 is an upper bound for the distance between two slopes on m whose associated fillings are not hyperbolic manifolds in this paper we verify the conjecture when the first betti number of m is at least 2 by showing that given a pseudo anosov mapping class f of a surface and an essential simple closed curve in the surface then 5 is an upper bound for the diameter of the set of integers n for which the composition of f with the n th power of a dehn twist along is not pseudo anosov this sharpens an inequality of albert fathi for large manifolds m of first betti number 1 we obtain partial results set

universal power law tails for singularity dominated strong fluctuations integrals of the type i t identical to integral integral dxdy delta t h x y are considered where h is a function from an ensemble labelled by parameters i can represent circulation times of fluid particles in the plane orbital periods or semiclassical densities of states for one dimensional hamiltonian systems spectral densities for two dimensional crystals or the strength of a wave pulse produced by propagation of a deformed step discontinuity as h varies over the ensemble i develops strong fluctuations associated with legendre singularities for unrestricted functions h the probability distribution p i describing the fluctuations of i decays according to a universal i 9 law obtained by a scaling argument involving arnold s classification of catastrophes if h is only quadratic in y p varies as i 10 if the integral defining i is one dimensional p varies as i 3 if it is three dimensional i decays no faster than i 48 the probability distribution of i identical to mod delta i delta t mod decays as i 2

the space of incompressible surfaces in a 2 bridge link complement projective lamination spaces for 2 bridge link complements are computed explicitly in this paper we construct a polyhedron p s3 lp q whose rational points correspond bijectively in a natural way with the projective isotopy classes of incompressible surfaces in the exterior of a 2 bridge link lp q c s3 here projective means that we factor out by scalar multiplication taking any number of parallel copies of a surface surfaces are not assumed to be connected we expect that p s3 lp q will turn out to be the projective lamination space of s3 lp q33 as defined and studied for general compact irreducible 3 manifolds in 5 and 12 an unexpected complication not present in thurston s theory of projective lamination spaces for surfaces is the fact that p s3 lp q is frequently noncompact for example for the whitehead link l3 8 see figure 5 4 upper left hand corner however as in the general theory p s3 lp q has a natural compactification p7 53 lp q which is a finite polyhedron to construct p s3 lp q 3 we first find a fairly natural finite collection of branched surfaces bi c s3 lp q which carry all the incompressible surfaces in s3lp q to each bi is associated a convex cell ci whose rational points parametrize the projective classes of surfaces carried by bi diserent rational points of ci can determine isotopic surfaces however due to the possibility of pushing parts of surfaces across product regions in the complement of bi the analogue of digon regions in the complement of a train track on a surface this leads to a linear projection pi ci ci f ci onto another convex polyhedral cell ci such that over the interior of ci projective isotopy classes of surfaces coincide with fibers of pi however these isotopy relations may not persist over the boundary of ci namely passing to a face of ci corresponds to passing to a branched subsurface of bi and a nonproduct complementary region of this branched subsurface may be decomposed by bi into product complementary regions of bi in this case rational points of this face of ci correspond not to projective isotopy classes of incompressible surfaces but to incompressible surfaces with these limiting phantom isotopy relations the space p7 53 lp q is foed from the cells ci by identifying their faces in the most natural way distinguishing different phantom isotopies between the same sets of surfaces pz s3 lp q consists of the open cells of ps s3 lp q for which the phantom isotopies are actual isotopies received by the editors april 12 1986 1980 mathematics subject classification 1985 revtaion primary 57m25

an improved path integration method for nonlinear systems under poisson white noise excitation abstract in order to overcome some unsatisfactory trends and limitations of the traditional path integration pi method for poisson white noise a novel pi method is proposed in this paper which includes two improved schemes the first one is a new transition probability density function tpdf approximation which considers the randomness of the impulse happening time during each time intervals the second one is a transformation of chapman kolmogorov ck equation by a variable substitution instead of directly using it whose numerical calculation is based on the back stepping runge kutta scheme and the triangulation based interpolation monte carlo simulations mcs are utilized to measure the accuracy of the improved algorithm with three illustrative nonlinear systems the results show that compared with the traditional pi method the improved pi method can give a more accurate description of the tpdf values and provide more precise stationary probability density function pdf results whenever the mean arrival rate is large or small the improved algorithm has a wider range of choices in time interval values to maintain the accuracy of stationary pdf results besides it is discovered that cubic interpolation deserves to be applied in the improved pi method more than linear and natural interpolations

stochastic averaging of quasi partially integrable hamiltonian systems under combined gaussian and poisson white noise excitations abstract a stochastic averaging method for predicting the response of quasi partially integrable and non resonant hamiltonian systems to combined gaussian and poisson white noise excitations is proposed for the case with r 1 r n independent first integrals which are in involution an r dimensional averaged generalized fokker planck kolmogorov gfpk equation for the transition probability density of r independent first integrals is derived from the stochastic integro differential equations sides of the original quasi partially integrable and non resonant hamiltonian systems by using the stochastic jump diffusion chain rule and the stochastic averaging theorem an example is given to illustrate the applications of the proposed stochastic averaging method and a combination of the finite difference method and the successive over relaxation method is used to solve the reduced gfpk equation to obtain the stationary probability density of the system the results are well verified by a monte carlo simulation

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

one sided orthogonality orthomodular spaces quantum sets and a class of garside groups abstract the classification of orthomodular lattices by means of their structure group is extended to non symmetric orthogonality relations spaces with a non hermitian sesquilinear form quantum sets and a new class of garside groups are given as examples

on character varieties of two bridge knot groups we find explicit models for the psl2 c and sl2 c character varieties of the fundamental groups of complements in s of an infinite family of two bridge knots that contains the twist knots we compute the genus of the components of these character varieties and deduce upper bounds on the degree of the associated trace fields we also show that these knot complements are fibered if and only if they are commensurable to a fibered knot complement in a z 2z homology sphere resolving a conjecture of hoste and shanahan

on the heegaard floer homology of branched double covers abstract let l s 3 be a link we study the heegaard floer homology of the branched double cover l of s 3 branched along l when l is an alternating link hf of its branched double cover has a particularly simple form determined entirely by the determinant of the link for the general case we derive a spectral sequence whose e 2 term is a suitable variant of khovanov s homology for the link l converging to the heegaard floer homology of l

essential surfaces of non negative euler characteristic in genus two handlebody exteriors we provide a classification of the essential surfaces of non negative euler characteristic in the exteriors of genus two handlebodies embedded in the 3 sphere

totally geodesic seifert surfaces in hyperbolic knot and link complements ii the first examples of totally geodesic seifert surfaces are constructed for hyperbolic knots and links including both free and totally knotted surfaces then it is proved that two bridge knot complements cannot contain totally geodesic orientable surfaces

meridional surfaces and 1 1 knots we determine all 1 1 knots which admit an essential meridional surface namely we give a construction which produces 1 1 knots having essential meridional surfaces and show that if a 1 1 knot admits an essential meridional surface then it comes from the given construction