For a given p-valent analytic function g with positive coefficients in the open unit disk ∆, we study a class of functions f(z) = z + ∑∞ n=m anz , an ≥ 0 satisfying 1 p < ( z(f ∗ g)′(z) (f ∗ g)(z) ) < α ( z ∈ ∆; 1 < α < m+ p 2p ) . Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special ...

For any n > 1 and 0 < ε < 1/2, we show the existence of an n-point subset X of R such that any linear map from (X, `2) to ` m 2 with distortion at most 1 + ε must have m = Ω(min{n, ε−2 logn}). Our lower bound matches the upper bounds provided by the identity matrix and the Johnson-Lindenstrauss lemma [JL84], improving the previous lower bound of Alon [Alo03] by a log(1/ε) factor.

We present the enabling concept and technology for a dual spacecraft formation-flying optical interferometer, to be launched into a deep space orbit as Space Technology 3. The combiner spacecraft makes use of a nested cat’s eye delay line configuration that minimizes wavefront distortion and stores 20 m of optical pathlength in a package of ∼ 1.5 m length. A parabolic trajectory for the seconda...

Upon compressing perceptually relevant signals, conventional quantization generally results in unnatural outcomes at low rates. We propose distribution preserving quantization (DPQ) to solve this problem. DPQ is a new quantization concept that confines the probability space of the reconstruction to be identical to that of the source. A distinctive feature of DPQ is that it facilitates a seamles...

Trans. Inform. Theory, vol. IT-23, pp. 343-353, May 1977. [4] H. H. Tan, “Tree encoding of discrete-time abstract-alphabet stationary block-ergodic sources with a fidelity criterion,” IEEE Trans. Inform. Theory, vol. IT-22, pp. 671-681, Nov. 1976. [5] R. M. Gray, D. L. Net&off, and J. K. Omura, “Process definition of distortion-rate functions and source coding theorems,” IEEE Trans. Inform. The...

introduction echo-planar imaging (epi) is a group of fast data acquisition methods commonly used in fmri studies. it acquires multiple image lines in k-space after a single excitation, which leads to a very short scan time. a well-known problem with epi is that it is more sensitive to distortions due to the used encoding scheme. source of distortion is inhomogeneity in the static b0 field that ...

The anion photoelectron spectra of ortho-, meta-, and para-methylphenoxide, as well as methyl deprotonated meta-methylphenol, were measured. Using the Slow Electron Velocity Map Imaging technique, the Electron Affinities (EAs) of the o-, m-, and p-methylphenoxyl radicals were measured as follows: 2.1991±0.0014, 2.2177±0.0014, and 2.1199±0.0014 eV, respectively. The EA of m-methylenephenol was a...

1 Optimality theorems for JL Yesterday we saw for MJL that we could achieve target dimension m = O(ε −2 log N), and for DJL we could achieve m = O(ε −2 log(1/δ)). The following theorems tell us that not much improvement is possible for MJL, and for DJL we have the optimal bound. Theorem 1 ([Alo03]). For any N > 1 and ε < 1/2, there exist N + 1 points in R N such that achieving the MJL guarantee...