efficient parallel rooting of complex polynomials on the unit circle an efficient method is presented for rooting complex polynomial equations of any order where the root space is restricted to the unit circle the method restates the evaluation of polynomials as a recursive algorithm involving only additions by means of the bilinear transformation the straight line uniformly spaced recursive polynomials evaluation method of a h nuttall 1987 is extended to the unit circle where the root positions are determined by thresholding general coefficient transformations are provided along with a comparison to the horner method

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

the bilinear transformation of two dimensional state space systems many authors have used the two dimensional 2 d bilinear transformation to obtain 2 d digital filters from stable 2 d analog filters in this paper a technique is proposed for performing the bilinear transformation on 2 d state space systems this technique is also applicable to multidimensional mimo systems programming this algorithm is straightforward if there is access to computer subroutines that add multiply and invert matrices

transformation matrices in the general bilinear transformation of multivariable polynomials the structure of the transformation matrix t for the general bilinear transformation of a single variable polynomial is examined this is applied to produce an efficient algorithm for the transformation of a multivariable polynomial

on the kolmogorov s condition for a special case of the kirchhoff top in this article the classical kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered then for the corresponding hamiltonian system on the zero integral level the kolmogorov s condition which is important for kolmogorov arnold moser theory is checked in contrast to known similar results there exists a curve in the bifurcation diagram along which the kolmogorov s condition vanishes for certain values of the parameters

general spectral transformations for digital filters constantinides 1 gave a method of transforming a prototype low pass digital filter into a high pass bandpass or bandstop filter by conformally mapping the complex variable z 1 we generalize here his method to transformations from prototype low pass filters to filters containing any number of pass and stopbands the computation procedure involves only the solution of a set of simultaneous linear equations the number of which is related only to the number of band edges and not to the order of the prototype filter

the monotonicity of period function for codimension four quadratic system q4 abstract in this paper we study the codimension four quadratic system q 4 z iz 4 z 2 2 z 2 b ic z 2 where b and c are real constants i 2 1 z x iy b ic 2 it is proved that the period function of periodic trajectories for q 4 is monotone the content of this paper can be viewed as a contribution to the proof of chicone s conjecture cf mr 94h 58072

bilinear transformation of multivariable polynomials using the horner method the general bilinear transformation of a single variable polynomial using the horner method of synthetic division has been described by davies 1974 and by policastro 1979 the procedure which is very simple to apply is extended to multivariable polynomials

criteria to bound the number of critical periods in the present paper we study the period function of centers of potential systems we obtain criteria to bound the number of critical periods in case that the system is polynomial our result enables to tackle the problem from a purely algebraic point of view since it allows to bound the number of critical periods by counting the zeros of a polynomial to illustrate its applicability some new and old results are proved

uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects abstract this paper considers the inverse problem of scattering of time harmonic acoustic and electromagnetic plane waves by a bounded inhomogeneous penetrable obstacle with embedded objects inside a new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far field pattern at a fixed frequency disregarding its contents our method is based on constructing a well posed interior transmission problem in a small domain associated with the helmholtz or modified helmholtz equation and the maxwell or modified maxwell equations a key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in l p 1 p 2 which are established in this paper by using the integral equation method a main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces

probing for electrical inclusions with complex spherical waves let a physical body in 2 or 3 be given assume that the electric conductivity distribution inside consists of conductive inclusions in a known smooth background further assume that a subset is available for boundary measurements it is proved using hyperbolic geometry that certain information about the location of the inclusions can be exactly recovered from static electric measurements on more precisely given a ball b with center outside the convex hull of and satisfying b boundary measurements on with explicitly given dirichlet data are enough to determine whether b intersects the inclusion an approximate detection algorithm is introduced based on the theory numerical experiments in dimension two with simulated noisy data suggest that the algorithm finds the inclusion free domain near and is robust against measurement noise 2007 wiley periodicals inc

a new transformation matrix for bilinear transformation a new transformation matrix technique is proposed for the bilinear transformation of polynomials the number of multiplications and additions involved in the new method is less than the number involved in the q matrix method of transformation

on the period function of reversible quadratic centers with their orbits inside quartics abstract this paper is concerned with the monotonicity of the period function for a class of reversible quadratic centers with their orbits inside quartics it is proved that such a system has a period function with at most one critical point

reachability of maximal number of critical periods without independence abstract the reachability of the maximal number of critical periods bifurcated from a weak center is judged with independence of period quantities since the independence is a sufficient condition in this paper we give a method to judge the reachability without the independence our main idea is to consider how the number of zeros for derivative of the period function changes as a curve in the parameter space scans near a specific point and choose an appropriate curve to find the largest number of zeros we apply this method to two polynomial differential systems having zero dimensional isochronicity variety and nonzero dimensional one separately to show that the maximal number is reached and obtain greater numbers than those obtained by classical independence separately with our method the two examples give the possibility that more critical periods arise from an isochronous center than a finite order weak center an opposite fact to many known results

perturbation from an elliptic hamiltonian of degree four iv figure eight loop the paper deals with lienard equations of the form x y y p x yq x with p and q polynomials of degree respectively 3 and 2 attention goes to perturbations of the hamiltonian vector fields with an elliptic hamiltonian of degree four exhibiting a figure eight loop it is proved that the least upper bound of the number of zeros of the related elliptic integral is five and this is a sharp bound multiplicity taken into account moreover if restricting to the level curves inside a saddle loop or outside the figure eight loop the sharp upper bound is respectively two or four also the multiplicity of the zeros is at most four this is the last one in a series of papers on this subject the results of this paper together with j differential equations 176 2001 114 j differential equations 175 2001 209 j differential equations to be published largely finish the study of the cubic perturbations of the elliptic hamiltonians of degree four and presumably provide a complete description of the number and the possible configurations of limit cycles for cubic lienard equations with small quadratic damping as a special case we obtain a configuration of four limit cycles surrounding three singularities together with a small limit cycle which surrounds one of the singularities

perturbations from an elliptic hamiltonian of degree four i saddle loop and two saddle cycle abstract the paper deals with lienard equations of the form x y y p x yq x with p and q polynomials of degree respectively 3 and 2 attention goes to perturbations of the hamiltonian vector fields with an elliptic hamiltonian of degree 4 and especially to the study of the related elliptic integrals besides some general results the paper contains a complete treatment of the saddle loop case and the two saddle cycle case it is proven that the related elliptic integrals have at most two zeros respectively one zero the multiplicity taken into account the bifurcation diagram of the zeros is also obtained

recursive algorithms for two dimensional filters spectral transformations in this correspondence a fast algorithm for two dimensional 2 d digital filters spectral transformations is developed the whole algorithm is based on the 1 d and 2 d horner s form all the considered spectral transformations are arbitrary 2 d rational transformations the method is successfully applied in an example concerning 2 d digital filter design

an fft algorithm based fast algorithm for arbitrary polynomial transformation a fast algorithm for the arbitrary polynomial transformation is described this algorithm is based on the fast fourier transform fft algorithm and reduces the computational complexity of a recently proposed recursive algorithm by an order of magnitude

on the number of critical periods for planar polynomial systems abstract in this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one we give a method which lets us prove that there are planar polynomial centers of degree l with at least 2 l 2 2 critical periods as well as study concrete families of potential reversible and lienard centers this last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not increases with the order of the perturbation

gradient estimates for solutions to divergence form elliptic equations with discontinuous coefficients in this paper we derive global w1 and piecewise c1 estimates for solutions to divergence form elliptic equations with piecewise holder continuous coefficients the novelty of these estimates is that even though they depend on the shape and on the size of the surfaces of discontinuity of the coefficients they are independent of the distance between these surfaces

the period function for quadratic integrable systems with cubic orbits this paper is concerned with the monotonicity of the period function for families of quadratic systems with centers whose orbits lie on cubic planar curves it is proved that each such system has a period function with at most one critical point

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

reconstruction of a penetrable obstacle by complex spherical waves we consider an inverse acoustic scattering problem for identifying a non convex penetrable obstacle in three dimensions in a homogeneous medium we apply the complex geometrical optics solutions with logarithmic phase which is called complex spherical waves to reconstruction problem the reconstruction schemes will be demonstrated in the last section

a simple algorithm for arbitrary polynomial transformation a very simple algorithm is developed for the arbitrary rational transformation of a polynomial the fact that many of the multiplications performed involve one zero factor is not explicitly taken into account if desired this could be done with some increase in the complexity of the algorithm itself finally if roundoff error is expected to be a problem double precision arithmetic could be used

on the evaluation of double square integral in the s 1 s 2 complex biplane in this correspondence a method of evaluating the double square integral int min 0 max infin int min 0 max infin h t 1 t 2 2 dt 1 dt 2 frac 1 2 pij 2 int min j infin max j infin int min j infin max j infin h s 1 s 2 ds 1 ds 2 where h t 1 t 2 l 1 h s 1 s 2 is discussed the method of evaluation is based on using the double bilinear transformation dbt s k 1 z k 1 z k k 1 2 to reduce the above complex integral to a double integral in the complex z 1 z 2 bidisk sum min m 0 max infin sum min n 0 max infin a m n 2 frac 1 2 pij 2 oint min z1 1 oint min z2 1 a z 1 z 2 cdot a z 1 1 z 2 1 frac dz 1 z 1 frac dz 1 z 2 there exist several methods for evaluating the above double integral in this correspondence we mention one promising method also a matrix method is proposed for applying the dbt to a quotient of two dimensional 2 d polynomials

first derivative of the period function with applications abstract given a centre of a planar differential system we extend the use of the lie bracket to the determination of the monotonicity character of the period function as far as we know there are no general methods to study this function and the use of commutators and lie bracket was restricted to prove isochronicity we give several examples and a special method which simplifies the computations when a first integral is known

a new algorithm for arbitrary transformation of polynomial and rational functions a new algorithm for performing the arbitrary polynomial transformation for single and multiple variables is presented it is based on the polynomial interpolation of the numerator and the denominator polynomials of the rational functions at the roots of unity using the discrete fourier transform dft by proper modification of the algorithm it is possible to compute the q matrix of the transformation generalization of the algorithm to higher dimensions is also presented

determining a magnetic schrodinger operator from partial cauchy data in this paper we show in dimension n 3 that knowledge of the cauchy data for the schrodinger equation in the presence of a magnetic potential measured on possibly very small subsets of the boundary determines uniquely the magnetic field and the electric potential we follow the general strategy of 7 using a richer set of solutions to the dirichlet problem that has been used in previous works on this problem

the cyclicity of quadratic reversible systems with a center of genus one and non morsean point in this paper we investigate a quadratic reversible system with non morsean point it is proved that the cyclicity of the period annulus under quadratic perturbations is less or equal to four