We present here strong numerical and statistical evidence of the fact that the Smale’s 7th problem can be answered affirmatively. In particular, we show that a local minimum for the logarithmic potential energy in the 2-sphere satisfying the Smale’s conditions can be identified with a computational cost of approximately O(N10).

In the present work, we aim to introduce and investigate a novel comprehensive subclass of normalized analytic bi-univalent functions involving Gegenbauer polynomials zero-truncated Poisson distribution. For in aforementioned class, find upper estimates second third Taylor–Maclaurin coefficients, then solve Fekete–Szegö functional problem. Moreover, by setting values parameters included our mai...

We discuss some theoretical aspects of the univariate case of the method recently introduced by Sommariva and Vianello [12] for the calculation of approximate Fekete points for polynomial interpolation.

In this paper, we obtain initial coefficient bounds for functions belong to a comprehensive subclass of univalent functions by using the Chebyshev polynomials and also we find Fekete-Szegö inequalities for this class. All results are sharp.

In this paper, we prove that for a bounded domain Ω in a rank-1 symmetric space, the first non-zero Neumann eigenvalue μ1(Ω) ≤ μ1(B(r1)) where B(r1) denotes the geodesic ball of radius r1 such that vol(Ω) = vol(B(r1)) and equality holds iff Ω = B(r1). This result generalises the works of Szego, Weinberger and Ashbaugh-Benguria for bounded domains in the spaces of constant curvature.

In this paper we present a procedure for the estimation of the Fekete points on a wide variety of non-regular objects in IR. We understand the problem of the Fekete points in terms of the identification of good equilibrium configurations for a potential energy that depends on the relative position of N particles. Although the procedure that we present here works well for different potential ene...

MedicalOne, Elwood, VIC. Eva Szego, MB BS, General Practitioner. Reprints will not be available from the author. Correspondence: Dr Eva Szego, MedicalOne, 61–69 Brighton Road, Elwood, VIC 3184. [email protected] The Medical Journal of Australia ISSN: 0025729X 5 July 2004 181 1 21-22 ©The Medical Journal of Australia 2004 www.mja.com.au The Profession – 90th Anniversary And so I began my c...

Let X be a Spin manifold with boundary, such that the Spin structure is defined near the boundary by an almost complex structure, which is either strictly pseudoconvex or pseudoconcave (and hence contact). Using generalized Szego projectors, we define modified partial differential-Neumann boundary conditions, Reo, for spinors, which lead to subelliptic Fredholm boundary value problems for the S...