rogers ramanujan and the baker gammel wills pade conjecture in 1961 baker gammel and wills conjectured that for functions f meromorphic in the unit ball a subsequence of its diagonal pade approximants converges uniformly in compact subsets of the ball omitting poles of f there is also apparently a cruder version of the conjecture due to pade himself going back to the early twentieth century we show here that for carefully chosen q on the unit circle the rogers ramanujan continued fraction

omni optimizer a generic evolutionary algorithm for single and multi objective optimization due to the vagaries of optimization problems encountered in practice users resort to different algorithms for solving different optimization problems in this paper we suggest and evaluate an optimization procedure which specializes in solving a wide variety of optimization problems the proposed algorithm is designed as a generic multi objective multi optima optimizer care has been taken while designing the algorithm such that it automatically degenerates to efficient algorithms for solving other simpler optimization problems such as single objective uni optimal problems single objective multi optima problems and multi objective uni optimal problems the efficacy of the proposed algorithm in solving various problems is demonstrated on a number of test problems chosen from the literature because of its efficiency in handling different types of problems with equal ease this algorithm should find increasing use in real world optimization problems

on rational approximation of algebraic functions abstract we construct a new scheme of approximation of any multivalued algebraic function f z by a sequence r n z n n of rational functions the latter sequence is generated by a recurrence relation which is completely determined by the algebraic equation satisfied by f z compared to the usual pade approximation our scheme has a number of advantages such as simple computational procedures that allow us to prove natural analogs of the pade conjecture and nuttall s conjecture for the sequence r n z n n in the complement cp 1 d f where d f is the union of a finite number of segments of real algebraic curves and finitely many isolated points in particular our construction makes it possible to control the behavior of spurious poles and to describe the asymptotic ratio distribution of the family r n z n n as an application we settle the so called 3 conjecture of egecioglu et al dealing with a 4 term recursion related to a polynomial riemann hypothesis

spurious poles in pade approximation in the theory of pade approximation locally uniform convergence has been proved only for special classes of functions for much larger classes convergence in capacity has been shown to hold true the reason for one type of convergence to hold true but the other one not can be found in poles of the approximants that may occur apparently anywhere in the complex plane because of their unwanted nature and since they do not correspond to singularities of the function f to be approximated these poles are called spurious the denominators of pade approximants satisfy orthogonality relations and consequently the location and distribution of spurious poles depend on properties of the orthogonality relations in the present paper the possibility of spurious poles is studied from the perspective of these orthogonal relations

embedding compact three dimensional cr manifolds of finite type in mathbf c n an abstract three dimensional cr manifold x is a smooth manifold without boundary of real dimension three equipped with a smooth one dimensional complex sub bundle t0 of its complexified tangent bundle which for each x e x satisfies txol n txo 1 o canonically associated to the cr structure is a first order differential operator db which maps functions on x to sections of the bundle b 1 dual to to and is defined by

estimates for the bar partial neumann problem in pseudoconvex domains of finite type in c2problem in pseudoconvex domains of finite type in c2

fundamental solutions for second order subelliptic operators estimation de la solution fondamentale d un operateur aux derivees partielles lineaire du second ordre sur une variete compacte avec une mesure reguliere

on the regularity of inverses of singular integral operators sur r d on considere un operateur de convolution sf f k ou k est une distribution homogene de degre d on suppose que s s etend a un operateur borne et inversible sur l 2 r d l inverse de s est donne par convolution avec une distribution l aussi homogene de degre d on montre qu une regularite possedee par k est partagee par l

maximal hypoellipticity for the neumann problem abstract we establish maximal hypoellipticity for the neumann problem on smooth bounded pseudoconvex domains in c n under the weakest possible condition on the levi form in particular maximal hypoellipticity holds on the level of n 1 forms for pseudoconvex domains of finite commutator type

estimates for the parametrix of the kohn laplacian on certain domains soit le demi espace superieur degenere generalise dans c 3 d p w 1 w 2 w imw p w 1 w 2 2 ou p c p 0 0 p est reel p 0 p 0 0 k p 0 0 pour k 2 on etudie la taille de la solution fondamentale de b sur des formes 0 1 sur la frontiere de d p

transfer matrices and partition function zeros for antiferromagnetic potts models i general theory and square lattice chromatic polynomial we study the chromatic polynomials zero temperature antiferromagnetic potts model partition functions p g q for m n rectangular subsets of the square lattice with m 8 free or periodic transverse boundary conditions and n arbitrary free longitudinal boundary conditions using a transfer matrix in the fortuin kasteleyn representation in particular we extract the limiting curves of partition function zeros when n which arise from the crossing in modulus of dominant eigenvalues beraha kahane weiss theorem we also provide evidence that the beraha numbers b2 b3 b4 b5 are limiting points of partition function zeros as n whenever the strip width m is 7 periodic transverse b c or 8 free transverse b c along the way we prove that a noninteger beraha number except perhaps b10 cannot be a chromatic root of any graph

conjecture on the interlacing of zeros in complex sturm liouville problems the zeros of the eigenfunctions of self adjoint sturm liouville eigenvalue problems interlace for these problems interlacing is crucial for completeness for the complex sturm liouville problem associated with the schrodinger equation for a non hermitian pt symmetric hamiltonian completeness and interlacing of zeros have never been examined this paper reports a numerical study of the sturm liouville problems for three complex potentials the large n limit of a ix n potential a quasiexactly solvable x4 potential and an ix3 potential in all cases the complex zeros of the eigenfunctions exhibit a similar pattern of interlacing and it is conjectured that this pattern is universal understanding this pattern could provide insight into whether the eigenfunctions of complex sturm liouville problems form a complete set