LetGn,r(K) be the Grassmannian manifold of k-dimensionalK-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. We consider the Radon, cosine and sine transforms, Rr′,r, Cr′,r and Sr′,r, from the L space L2(Gn,r(K)) to the space L 2(Gn,r′(K)), for r, r ′ ≤ n − 1. The L spaces are decomposed into irreducible representations of G with multiplicity free. We compute ...

It is shown that K|ω1 need not be solid in the sense of [FS]: It is consistent that there is no inner model with a Woodin cardinal yet there is an inner model W and a Cohen real x over W such that K|ω1 ∈ W [x] \ W . However, if 0¶ does not exist and κ ≥ ω2 is a cardinal, then K|κ is solid. We draw the conclusion that solidity is not forcing absolute in general, and that under the assumption of ...

The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk, [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the considered variants) this is the best result we can expec...

1. Error calculus 2 1.1. Ulp calculus 2 1.2. Relative error analysis 4 1.3. Generic error of addition/subtraction 4 1.4. Generic error of multiplication 5 1.5. Generic error of inverse 5 1.6. Generic error of division 6 1.7. Generic error of square root 7 1.8. Generic error of the exponential 7 1.9. Generic error of the logarithm 8 1.10. Ulp calculus vs relative error 9 2. Low level functions 9...

It is well known that in applied and computational mathematics, cardinal B-splines play an important role in geometric modeling (in computeraided geometric design), statistical data representation (or modeling), solution of differential equations (in numerical analysis), and so forth. More recently, in the development of wavelet analysis, cardinal B-splines also serve as a canonical example of ...

An assumption commonly made in the study of visual perception is that the lower the contrast threshold for a given stimulus, the more sensitive and selective will be the mechanism that processes it. On the basis of this consideration, we investigated contrast thresholds for two classes of stimuli: sine-wave gratings and radial frequency stimuli (i.e., j0 targets or stimuli modulated by spherica...

Many hardware algorithms exist to handle the hardware intensive signal processing problems. Among these algorithms is a set of shift-add algorithms collectively known as CORDIC for computing a wide range of functions including certain trigonometric, hyperbolic, linear and logarithmic functions. While there are numerous articles covering various aspects of CORDIC algorithms, very few survey more...