scattering of sound from axisymetric sources by multiple circular cylinders a general analytic method for calculating the scattering of sound by multiple rigid circular cylinders arranged in an arbitrary parallel configuration is presented the sound scattered by this collection of cylinders is generated by a time periodic spatially distributed axisymmetric source located within the domain of interest a hankel transform method is used to calculate the incident field while separation of variables is used to obtain the scattered fields from each cylinder in the collection the unknown scattering coefficients are determined through the use of general addition theorems that allows the various fields to be readily transformed between coordinate systems the method is validated using various two three and four cylinder configurations and the number of coefficients that must be retained in the truncated series is examined benchmark configurations consisting of two and three cylinder systems with cylinders of varying radii are also presented these solutions have been used to validate computational aeroacoustic solvers developed for complex geometries

coupling of dirichlet to neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering the applicability of the dirichlet to neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape the original boundary value problem bvp for the multiple scattering problem is reformulated as an interface bvp a heterogenous medium with variable physical properties in the vicinity of the obstacles is considered a rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given the problem is written in terms of generalized curvilinear coordinates inside the computational region then novel elliptic grids conforming to complex geometrical configurations of several two dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained the numerical method developed is validated by comparing the approximate and exact far field patterns for the scattering from two circular obstacles in this case for a second order finite difference scheme a second order convergence of the numerical solution to the exact solution is easily verified

the extreme points of the set of decreasing failure rate distributions since the class of extended decreasing failure rate edfr life distributions i e distributions with support in 0 is compact and convex it follows from choquet s theorem that every edfr life distribution can be represented as a mixture of extreme points of the edfr class we identify the extreme points of this class and of the standard class of decresing failure rate dfr life distributions further we show that even though the convex class of dfr life distributions is not compact every dfr life distribution can be represented as a mixture of extreme points of the dfr class

common limits of fibonacci circle maps we show that limits for the critical exponent tending to exist in both critical circle homeomorphism of golden mean rotation number and fibonacci circle coverings moreover they are the same the limit map is not analytic at the critical point which is flat but has non trivial complex dynamics

dynamics and universality of unimodal mappings with infinite criticality we consider infinitely renormalizable unimodal mappings with topological type which are periodic under renormalization we study the limiting behavior of fixed points of the renormalization operator as the order of the critical point increases to infinity it is shown that a limiting dynamics exists with a critical point that is flat but still having a well behaved analytic continuation to a neighborhood of the real interval pinched at the critical point we study the dynamics of limiting maps and prove their rigidity in particular the sequence of fixed points of renormalization for finite criticalities converges uniformly on the real domain to a mapping of the limiting type

maximum likelihood estimation for two parameter decreasing hazard rate distributions using censored data abstract problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions typically either mixed exponential or work hardened sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure even with highly censored data that the mle s exist from such dhr distributions whenever the sample satisfies a certain condition otherwise a constant hazard rate is estimated as a limiting case some computational methods are given and applications made

theoretical explanation of observed decreasing failure rate pooled data on the times of successive failures of the air conditioning system of a fleet of jet airplanes seemed to indicate that the life distribution had a decreasing failure rate more refined analysis showed that the failure distribution for each airplane separately was exponential but with a different failure rate using the theorem that a mixture of distributions each having a non increasing failure rate e g a mixture of exponential distributions itself has a non increasing failure rate the apparent decreasing failure rate of the pooled air conditioning life distribution was satisfactorily explained the present study has implications in other areas where an observed decreasing failure rate may well be the result of mixing exponential distributions having different parameters

displacement theorems for spherical solutions of the linear navier stokes equations displacement theorems are presented for the solutions in spherical coordinates of the linear navier stokes equations for time independent flow in an incompressible viscous fluid the theorems allow one to expand spherical solutions about a chosen center into spherical solutions centered elsewhere

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

acoustic scattering by two spheres multiple scattering and symmetry considerations abstract acoustic scattering by two identical spheres is theoretically numerically and experimentally studied by highlighting the role of the symmetries of the scatterer incident and scattered fields are expanded over the different irreducible representations of d h the continuous symmetry group of the scatterer then from the boundary conditions one obtains for each irreducible representation an infinite system of linear complex algebraic equations where the unknown scattering coefficients are uncoupled this feature greatly simplifies the treatment of the problem and speeds up calculations farfield form functions are computed in the cases of neumann boundary conditions rigid spheres and elastic boundary conditions elastic spheres immersed in water a series of experiments based on ultrasonic spectroscopy is performed in the case of two stainless steel spheres immersed in water the comparison between the theoretical and the experimental results provides quite a good agreement

an alternative expression for the addition theorems of spherical wave solutions of the helmholtz equation an alternative formulation of the addition theorem for spherical wave solutions of the helmholtz equation is presented the 3 j symbols of wigner or more precisely the gaunt coefficient complete solid angle integral of a triple product of spherical harmonics which appear in the formerly introduced expressions of these addition theorems are replaced by an explicit matrix expression relating the spherical wave solutions defined with respect to the different origins the generalized gaunt coefficients which are complete solid angle integrals of a multiple product of spherical harmonics can then be written in terms of a matrix product of basic matrices representing the gaunt coefficient

algebraic aspects of multiple scattering by two parallel cylinders classification and physical interpretation of scattering resonances abstract acoustic scattering by a pair of identical parallel cylinders is studied by emphasizing the role of the symmetries of the scatterer incident and scattered fields are expanded over the different irreducible representations ofc2v the symmetry group of the scatterer then from the boundary conditions one obtains an infinite set of four linear complex algebraic equations each one associated with a representation where the unknown coefficients of the scattered fields are uncoupled this method significantly simplifies the numerical treatment of the problem as a consequence positions of the scatterer resonances are determined in the complex plane of the reduced frequency and a partial algebraic classification of the resonances is obtained for various boundary conditions soft cylinders hard cylinders and elastic cylinders immersed in water a physical interpretation of certain resonances in terms of trapped geometrical paths is provided

addition theorems for spherical wave solutions of the vector helmholtz equation addition theorems for spherical wave solutions of the vector helmholtz equation are discussed the theorems allow one to expand a vector spherical wave about a given origin into spherical waves about a shifted origin a simplified derivation of the results obtained earlier by cruzan o r cruzan q appl math 20 33 1962 is presented

integral theorems in linear elastodynamics abstract we derive antenna theorems in elastodynamics for the displacement field generated by a force density located at a spherical surface on the basis of these theorems we derive an expression for an integral of the green s function of linear elastodynamics the integral corresponds to the so called overlap kernel which plays a key role in the cluster expansion approach in the statistical theory of elastic suspensions of spherical particles in elastostatics the integral is closely related to mean field expressions for the effective elastic moduli a factorized form of the overlap kernel in terms of vector spherical waves is derived

universality of critical circle covers for a class of critical circle covers we show that properly re scaled first return maps to a neighborhood of the critical point converge to universal limits for that to occur the critical point has to be sufficiently flat

an integral theorem in linear hydrodynamics abstract we derive an expression for an integral of the green s function of linear hydrodynamics the integral corresponds to the so called overlap kernel which plays a key role in the statistical theory of suspensions of spherical particles we derive a factorized form of the overlap kernel in terms of vector spherical waves

an integral equation approach to three dimensional acoustic radiation and scattering problems this paper provides numerical implementation and tests for a boundary integral equation method proposed recently by krutitskii ima j appl math 64 259 269 2000 for evaluating three dimensional acoustic radiation and scattering fields in the exterior neumann problem for several obstacles auxiliary boundaries with certain prescribed boundary conditions are introduced inside the obstacles for the purpose of eliminating the fictitious characteristic frequencies applying the simple source formulation on all boundaries leads to a set of uniquely solvable integral equations with weakly singular kernels to facilitate the numerical implementation the modified integral equations are further transformed to ordinary ones that contain nonsingular kernels only test cases consist of the acoustic radiation and scattering by one sphere and a pair of equal spheres comparisons are made with analytical solutions and schenck s chief method numerical results demonstrate the efficiency robustness and accuracy of

statistics of optical coherence tomography data from human retina optical coherence tomography oct has recently become one of the primary methods for noninvasive probing of the human retina the pseudoimage formed by oct the so called b scan varies probabilistically across pixels due to complexities in the measurement technique hence sensitive automatic procedures of diagnosis using oct may exploit statistical analysis of the spatial distribution of reflectance in this paper we perform a statistical study of retinal oct data we find that the stretched exponential probability density function can model well the distribution of intensities in oct pseudoimages moreover we show a small but significant correlation between neighbor pixels when measuring oct intensities with pixels of about 5 m we then develop a simple joint probability model for the oct data consistent with known retinal features this model fits well the stretched exponential distribution of intensities and their spatial correlation in normal retinas fit parameters of this model are relatively constant along retinal layers but varies across layers however in retinas with diabetic retinopathy large spikes of parameter modulation interrupt the constancy within layers exactly where pathologies are visible we argue that these results give hope for improvement in statistical pathology detection methods even when the disease is in its early stages

elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout in this paper based on the theory of elastic wave motion for open cylindrical shell wave scattering and dynamic stress concentrations in open cylindrical shells with a hole are studied by making use of small parameter perturbation methods and boundary integral equation techniques the boundary integral equations and iterative imminent series of scattered waves around the cavity of the cylindrical shell are derived by employing this method the approximately analytical solutions of scattered waves on the edge of cutout are gained the computational formula for getting the dynamic stress concentration factors on the contour of cavity is developed as an example the numerical results of these dynamic stress concentration factors are graphically presented and discussed the analytical methods put forward in the present work have practical significances for solving the problem of elastic wave scattering and dynamic stress concentrations in cylindrical shells with a circular cutout

rigidity of critical circle mappings ii we prove that two c3 critical circle maps with the same rotation number in a special set are c1 conjugate for some 0 provided their successive renormalizations converge together at an exponential rate in the c0 sense the set has full lebesgue measure and contains all rotation numbers of bounded type by contrast we also give examples of c critical circle maps with the same rotation number that are not c1 conjugate for any 0 the class of rotation numbers for which such examples exist contains diophantine numbers

dimensions and measures in infinite iterated function systems the hausdorff and packing measures and dimensions of the limit sets of iterated function systems generated by countable families of conformal contractions are investigated conformal measures for such systems reflecting geometric properties of the limit set are introduced proved to exist and to be unique the existence of a unique invariant probability equivalent to the conformal measure is derived our methods employ the concepts of the perron frobenius operator symbolic dynamics on a shift space with an infinite alphabet and the properties of the above mentioned ergodic invariant measure a formula for the hausdorff dimension of the limit set in terms of the pressure function is derived fractal phenomena not exhibited by finite systems are shown to appear in the infinite case in particular a variety of conditions are provided for hausdorff and packing measures to be positive or finite and a number of examples are described showing the appearance of various possible combinations for these quantities one example given special attention is the limit set associated to the complex continued fraction expansion in particular lower and upper estimates for its hausdorff dimension are given a large natural class of systems whose limit sets are dimensionless in the restricted sense is described

hausdorff dimension of julia sets of feigenbaum polynomials with high criticality we consider unimodal polynomials with feigenbaum topological type and critical points whose orders tend to infinity it is shown that the hyperbolic dimensions of their julia set go to 2 furthermore that the hausdorff dimensions of the basins of attraction of their feigenbaum attractors also tend to 2 the proof is based on constructing a limiting dynamics with a flat critical point