• Korean Journal of Mathematics
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• v.18 no.2
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• pp.149-160
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• 2010

Let $W(x)={\prod}_{k=1}^m{\mid}x-x_k{\mid}^{{\gamma}_k}{\cdot}{\exp}(-{\mid}x{\mid}^{\alpha})$. Associated with the weight W, upper and lower bounds of the generalized Christoffel functions for generalized nonnegative polynomials are obtained.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.121-134
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• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• Magazine of the Korean Society of Agricultural Engineers
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• v.18 no.1
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• pp.4071-4078
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• 1976

The authors analyzed the seepage by means of the following mathmatical solutions of the Laplace Equations on the given boundary conditions. The boundaries of the flow region are of two types i) impervious boundaries (${\Phi}$=constant), and ii) reservoir boundaries (${\Phi}$=constant). The corresponding w plane, bounding the flow region, is the rectangle in Fig. 8-a. As the z plane and w plane are both polygons, by means of the Schwarz-Christoffel transformation the flow region in each of these planes can be mapped con for mally onto the same half of an auxiliary t plane, there by yielding, say, the functions z=f1(t) and w=f2(t). Then, either by eliminating the variable t or by using t as a parameter, the function w=f(z) can be established.