a regularized sampling method for solving three dimensional inverse scattering problems the inverse scattering problem under consideration is to determine the shape of an obstacle in re 3 from a knowledge of the time harmonic incident acoustic wave and the far field pattern of the scattered wave with frequency in the resonance region a method for solving this nonlinear and improperly posed problem is presented which is based on solving a linear integral equation of the first kind and avoids the use of nonlinear optimization methods numerical examples are given showing the practicality of this new approach

connected floer homology of covering involutions using the covering involution on the double branched cover of s 3 branched along a knot and adapting ideas of hendricks manolescu and hendricks hom lidman we define new knot concordance invariants and apply them to deduce novel linear independence results in the smooth concordance group of knots

recent developments in inverse acoustic scattering theory we survey some of the highlights of inverse scattering theory as it has developed over the last 15 years with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects

interaction of a hopf bifurcation and a symmetry breaking bifurcation stochastic potential and spatial correlations the multivariate master equation for a general reaction diffusion system is solved perturbatively in the stationary state in a range of parameters in which a symmetry breaking bifurcation and a hopf bifurcation occur simultaneously thestochastic potential u is in general not analytic however in the vicinity of the bifurcation point and under precise conditions on the kinetic constants it is possible to define a fourth order expansion ofu around the bifurcating fixed point under these conditions the domains of existence of different attractors including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors are determined analytically the role of fluctuations in the existence and stability of the various patterns is pointed out

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

the slice ribbon conjecture for 3 stranded pretzel knots we determine the smooth concordance order of the 3 stranded pretzel knots p p q r with p q r odd we show that each one of finite order is in fact ribbon thereby proving the slice ribbon conjecture for this family of knots as corollaries we give new proofs of results first obtained by fintushel stern and casson gordon

a fast method for acoustic imaging of multiple three dimensional objects this paper is concerned with the inverse problem for imaging multiple three dimensional objects using the information of the far field pattern of the scattered wave a spatially dependent function which has noticeably different values inside and outside the obstacle is derived a numerical method based on the characterization is developed to obtain a visualization of the obstacle the most remarkable advantage of this method is that it does not need any prior knowledge about the geometry and physical properties of the scatterer and requires only the information of the far field measurements for a finite number of directions of incidence and observation distributed over a limited range furthermore the scheme is very simple and fast since it avoids the use of the iterative procedure and requires only the solution of a linear system some numerical examples with synthetic far field data are given showing the practicality and efficiency of this scheme

embedding seifert manifolds in s 4 using an obstruction based on donaldson s theorem on the intersection forms of definite 4 manifolds we determine which connected sums of lens spaces smoothly embed in s4 we also find constraints on the seifert invariants of seifert 3 manifolds which embed in s4 when either the base orbifold is non orientable or the first betti number is odd in addition we construct some new embeddings and use these along with the d and invariants to examine the question of when the double branched cover of a 3 or 4 strand pretzel link embeds

the lens space realization problem we determine the lens spaces that arise by integer dehn surgery along a knot in the three sphere specically if surgery along a knot produces a lens space then there exists an equivalent surgery along a berge knot with the same knot floer homology groups this leads to sharp information about the genus of such a knot the arguments rely on tools from floer homology and lattice theory they are primarily combinatorial in nature

three dimensional time harmonic electromagnetic inverse scattering the reconstruction of the shape and the impedance of an obstacle abstract a numerical method for the reconstruction of the shape and the impedance of an obstacle from time harmonic electromagnetic scattering data is presented let d be a bounded simply connected domain contained in the three dimensional euclidean space r 3 with smooth boundary d the three dimensional euclidean space is filled with an isotropic homogeneous medium we assume that d contains the origin and d is regarded as an obstacle whose electric properties are given by a boundary impedance x x d from the knowledge of the electric far fields generated by the obstacle d when hit by known time harmonic electromagnetic waves the shape d and the boundary impedance x of the obstacle are reconstructed the reconstruction algorithm is based on the herglotz function method introduced by colton and monk 1 in acoustic scattering

a new optimal control approach for the reconstruction of extended inclusions the aim of this paper is to propose a new regularized optimal control formulation for recovering an extended inclusion from boundary measurements our approach provides an optimal representation of the shape of the inclusion it guarantees local lipschitz stability for the reconstruction problem some numerical experiments are performed to demonstrate the validity and the limitations of the proposed reconstruction method

stochastic analysis of a hopf bifurcation master equation approach the effect of inhomogeneous fluctuations in a reaction diffusion system exhibiting a hopf bifurcation is analyzed using the master equation approach a taylor expansion of the logarithm of the stationary probability known as the stochastic potential is calculated this procedure displays marked analogies with the theory of normal forms the critical potential reduced to its local expansion around an arbitrary point of the limit cycle brings out the essential role played by the phase of the oscillating variables a comparison with the langevin analysis of walgraefet al j chem phys 78 6 3043 1983 is performed

the orientation of yang mills moduli spaces and 4 manifold topology si x est une 4 variete lisse orientee fermee dont la forme intersection q h 2 x z torsion z est definie negative alors la forme est equivalente sur les entiers a la forme standard 1 1 1 soit x une 4 variete lisse orientee fermee avec les trois proprietes suivantes 1 h 1 x z n a pas de 2 torsion 2 la forme intersection q sur h 2 x torsion a une partie positive de rang 1 ou 2 3 la forme intersection est paire alors q est equivalente sur les entiers a une des formes 01 10 01 10 01 10

equality governing nonequilibrium fluctuations and its information theory and thermodynamic interpretations the master equation is cast in the form of an equality involving the variation in the course of a transformation of a quantity playing the role of a generalized potential weighted with the probability of allowable transformations emanating from different initial states in the most general case this equality cannot be formulated entirely in terms of thermodynamic variables and state functions some conditions under which such a reduction becomes possible are identified and a comparison with fluctuation and work type relationships previously reported in the literature is carried out

stochastic analysis of symmetry breaking bifurcations master equation approach the multivariate master equation for a general reaction diffusion system is solved perturbatively in the vicinity of a bifurcation point leading to symmetry breaking transitions the possibility to express the result through a brazovskii type of potential is examined and a comparison with the langevin analysis of walgraefet al adv chem phys 49 311 1982 is performed

rational homology spheres and the four ball genus of knots using the heegaard floer homology of ozsvath and szabo we investigate obstructions to a rational homology sphere bounding a four manifold with a definite intersection pairing as an application we obtain new lower bounds for the four ball genus of montesinos links

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

three dimensional inverse obstacle scattering for time harmonic acoustic waves a numerical method a numerical method for a three dimensional inverse acoustic scattering problem is considered from the knowledge of several far fields patterns of the helmholtz equation a closed surface partial d representing the boundary of an unknown obstacle d is reconstructed the obstacle d is supposed to be acoustically soft or acoustically hard or characterized by a given acoustic impedance

absolutely graded floer homologies and intersection forms for four manifolds with boundary abstract in ozsvath and szabo holomorphic triangles and invariants for smooth four manifolds math sg 0110169 2001 we introduced absolute gradings on the three manifold invariants developed in ozsvath and szabo holomorphic disks and topological invariants for closed three manifolds math sg 0101206 ann of math 2001 to appear coupled with the surgery long exact sequences we obtain a number of three and four dimensional applications of this absolute grading including strengthenings of the complexity bounds derived in ozsvath and szabo holomorphic disks and three manifold invariants properties and applications math sg 0105202 ann of math 2001 to appear restrictions on knots whose surgeries give rise to lens spaces and calculations of hf for a variety of three manifolds moreover we show how the structure of hf constrains the exoticness of definite intersection forms for smooth four manifolds which bound a given three manifold in addition to these new applications the techniques also provide alternate proofs of donaldson s diagonalizability theorem and the thom conjecture for cp 2

donaldson s theorem heegaard floer homology and knots with unknotting number one abstract we establish an obstruction to unknotting an alternating knot by a single crossing change the obstruction is lattice theoretic in nature and combines donaldson s diagonalization theorem with an obstruction developed by ozsvath and szabo using heegaard floer homology as an application we enumerate the alternating 3 braid knots with unknotting number one and show that each has an unknotting crossing in its standard alternating diagram

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

nonequilibrium potentials near instabilities the existence of polynomial approximations for nonequilibrium potentials determined by a master equation near an instability of arbitrary codimension with diagonalizable linear part is studied it is shown that the approximations exist provided some relations are satisfied between the coefficients of the master equation

a simple global characterization for normal forms of singular vector fields we derive a new global characterization of the normal forms of amplitude equations describing the dynamics of competing order parameters in degenerate bifurcation problems using an appropriate scalar product in the space of homogeneous vector polynomials we show that the resonant terms commute with the group generated by the adjoint of the original critical linear operator this leads to a very efficient constructive method to compute both the nonlinear coefficients and the unfolding of the normal form explicit examples and results obtained when there are additional symmetries are also presented