A finite-dimensional commutative algebra A over a field K is called a Bernstein algebra if there exists a non-trivial homomorphism co: A -> K (baric algebra) such that the identity (x) = CO(X)JC holds in A (see [7]). The origin of Bernstein algebras lies in genetics (see [2,8]). Holgate (in [2]) was the first to translate the problem into the language of non-associative algebras. Information ab...

Let Bm(f) be the Bernstein polynomial of degree m. The Generalized Bernstein polynomials

It is shown that the modulation spaces Mwp can be characterized by approximation behavior of their elements using Local Fourier bases. In analogy to bases, we show also Gabor frames. We derive direct and inverse theorems describe best linear combinations N terms a given function its modulates translates.

We present a PAC-Bayes-Empirical-Bernstein inequality. The inequality is based on a combination of the PAC-Bayesian bounding technique with an Empirical Bernstein bound. We show that when the empirical variance is significantly smaller than the empirical loss the PAC-Bayes-Empirical-Bernstein inequality is significantly tighter than the PAC-Bayes-kl inequality of Seeger (2002) and otherwise it ...

A personal coach to help your most promising executives reach their potential--sounds good, doesn't it? But, according to Steven Berglas, executive coaches can make a bad situation worse. Because of their backgrounds and biases, they ignore psychological problems they don't understand. Companies need to consider psychotherapeutic intervention when the symptoms plaguing an executive are stubborn...

We measure a sign interlacing phenomenon for Bessel sequences (uk) in L2 spaces terms of the Kantorovich–Rubinstein mass moving norm ‖uk‖KR. Our main observation shows that, quantitatively, rate at which ‖uk‖KR→0 heavily depends on Bernstein–Kolmogorov widths compact set Lipschitz functions. In particular, it dimension space. also establish lower bound convergence norms ‖uk‖X→0 basis/frame any ...

A first-order theory T has the Schröder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB property if and only if T is superstable and non-multidimensional. We also prove that among superstable theories T , the class of a-saturated models of T has the SB property if and only if T has no nomadic ...