Takayasu's arteritis associated with Wiskott-Aldrich syndrome.

A unique case of a Chinese boy with Wiskott-Aldrich syndrome (WAS) associated with Takayasu's arteritis is reported. He had eczema, epistaxis and recurrent infections since early infancy and was found to have thrombocytopenia, negative delayed-type skin hypersensitivity, low T cell number and impaired lymphocyte proliferation to phytohaemagglutinin and concanavalin A. He had high normal serum immunoglobulin (Ig)G and IgA with low IgM and isohaemagglutinin. He presented with hypertensive encephalopathy at 5.5 years of age and an aortogram demonstrated abdominal aortic aneurysm with bilateral stenosis of renal arteries resulting in renovascular hypertension. His hypertension was difficult to control medically and autotransplant of his kidneys to the iliac arteries was performed, but he died in the immediate postoperative period. The relationship between immunodeficiency and collagen-vascular disease was discussed.

Multidimensional chirp algorithms for computing Fourier transforms.

Continuous versions of the multidimensional chirp algorithms compute the function G(y)=F(My), where F(y) is the Fourier transform of a function f(x) of a vector variable x and M is an invertible matrix. Discrete versions of the algorithms compute values of F over the lattice L(2)=ML(1 ) from values of f over a lattice L(1), where L(2) need not contain the lattice reciprocal to L(1). If M is symmetric, the algorithms are multidimensional versions of the Bluestein chirp algorithm, which employs two pointwise multiplication operations (PMOs) and one convolution operation (CO). The discrete version may be efficiently implemented using fast algorithms to compute the convolutions. If M is not symmetric, three modifications are required. First, the Fourier transform is factored as the product of two Fresnel transforms. Second, the matrix M is factored as M=AB, where A and B are symmetric matrices. Third, the Fresnel transforms are modified by the matrices A and B and each modified transform is factored into a product of two PMOs and one CO.