One approach for computations with special functions in computer algebra is the systematic use of analytic functions whenever possible. This naturally leads to problems of how to answer questions about analytic functions in a fully eeective way. Such questions comprise the determination of the radius of convergence or the evaluation of the analytic continuation of the function at the endpoint o...

— Let (X, 0) be a germ of an analytic coherent set in R'. Assume that analytic functions g^ ...,^p generate ideal I(X)oThere exists an increasing function e : N -»• N such that, for any function/of class C*^ vanishing on X, there exist C-f unctions q>i, ..., <pp such that /=<pi .gi +... +<Py.^p. In this paper we investigate the problem of the estimation of e (r) in some special cases. Let (X, 0...

using the effective management tools that are relevant tothe organization’s needs for excellence has become so important for thecompanies to improve their performances and then increase customersatisfaction and gain market shares. quality function deployment is anefficient and powerful tool in design, development, and planning of products.the main function of quality function deployment is conv...

Introduction. Let G be an open subset of the Euclidean w-space E, Gi an open subset with compact closure in G. If n = 2 and G is the whole of E, an important circle of theorems in the theory of analytic functions associated with the names of Walsh, HartogsRosenthal, Lavrentiev, Keldych, and Mergelyan deals with the possibility of approximating analytic functions on Gi continuous on its closure,...

trace function 45, 46-48, 50, 51, 56, 62, 64 adapted stratification 12, 24, 26, 37, 38, 46, 48, 63, 121, 408 additive character sums 2, 7, 8, 111-158, 161-183, 270-280, 427-428 analytic rank 8, 443, 444, 445, 447, 449, 451, 453 analytic rank, geometric see "geometric analytic rank" analytic rank, quadratic see "quadratic analytic rank" Analytic Rank Theorem 445, 450-454 approximate trace fu...

an_eul is a new automatic method for simultaneous approximation of location, depth, and structural index (geometry) of magnetic sources. in the 2d case analytic signal is defined as a conjugate function whose imaginary part is the hilbert transform of its real part. since the first vertical derivative of the magnetic field is the hilbert transform of its horizontal derivative, vertical and hori...

Analytic functions are characterized by the geometry of their image domains. That?s why, domain is substantial importance to have a comprehensive study analytic functions. To introduce and new geometrical structures as define subsequent an ongoing part research in geometric function theory. We introduced named cardioid defined corresponding function, see [14]. Here we further domain, starlike a...

An overview is presented on statistical techniques for the analytic evaluation of integrals for non-resonant, non-resonant depleted, non-resonant cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The techniques are based on statistical distribution theory and the theory of Meijer’s G-function and Fox’s H-function. The implementation of Meijer’s G-function in Mathematic...

the analytic signal method is a semiautomatic method for estimating the location of causative bodies in magnetic and gravity methods. the application of analytic signal for interpretation of two dimensional (2d) structures was introduced by nabighian (1972). the analytic signal is defined as a complex function in which the real and imaginary parts are a pair of hilbert transforms. in other word...