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Multivariate nonhomogeneous refinement equations (1999)

Dinsenbacher, Thomas B. ; Hardin, Douglas P.

Springer

The journal of Fourier analysis and applications 5 (1999), S. 589-597

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ISSN: 1531-5851

Keywords: 42C15 ; 39B99 ; multivariate ; nonhomogeneous ; refinement

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract We give necessary and sufficient conditions for the existence and uniqueness of compactly supported distribution solutionsf=(f 1,...,f r)T of nonhomogeneous refinement equations of the form $$f(x) = h(x) + \sum\limits_{\alpha \in A} {c_\alpha f(2x - \alpha )(x \in R^s )} $$ , where h=(h1,...,hr)Tis a compactly supported vector-valued multivariate distribution, A⊂Z+ s has compact support, and the coefficientsc α are real-valued r×r matrices. In particular, we find a finite dimensional matrix B, constructed from the coefficientsc α of the equation (I−B)q=p, where the vectorp depends on h. Our proofs proceed in the time domain and allow us to represent each solution regardless of the spectral radius of P(0):=2−s∑c α , which has been a difficulty in previous investigations of this nature.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01257193

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Human senescence (1996)

Kirkwood, Thomas B. L.

New York, NY : Wiley-Blackwell

BioEssays 18 (1996), S. 1009-1016

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ISSN: 0265-9247

Keywords: Life and Medical Sciences ; Cell & Developmental Biology

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Biology , Medicine

Notes: Human life expectancy has increased dramatically through improvements in public health, housing, nutrition and general living standards. Lifespan is now limited chiefly by intrinsic senescence and its associated frailty and diseases. Understanding the biological basis of the ageing process is a major scientific challenge that will require integration of molecular, cellular, genetic and physiological approaches. This article reviews progress that has been made to date, particularly with regard to the genetic contribution to senescence and longevity, and assesses the scale of the task that remains.

Additional Material: 5 Ill.