We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show that m-term nonlinear approximationwith the system in an α-modulation space can be completely characterized.

We show how to evaluate a bi-variate polynomial of degree n (i.e., having order n 2 many coefficients) at n generic points simultaneously within time O(n). This means an average cost of O(n) per point whereas a single evaluation provably requires in general Ω(n) operations.

We present a characterization of the local luminosity-color, bi-variate distribution of IRAS galaxies from the 1.2 Jy sample, selected at 60μm. The R(60,100) infrared color is used as the best single parameter description of the IR spectral energy distribution of galaxies. We derive an analytical form of the distribution and use it to constrain the effect of the IR color distribution on evoluti...

a variety of anthropometric and training characteristics have been identified as predictor variables for race performance in endurance and ultra-endurance athletes. anthropometric characteristics such as skin-fold thicknesses, body fat, circumferences and length of limbs, body mass, body height, and body mass index were bi-variately related to race performance in endurance athletes such as swim...

We construct orthonormal bases compatible with bi-variate homogeneous $$\alpha $$ -modulation spaces and the associated of Triebel–Lizorkin type. The construction is based on generating a separable -covering using carefully selected tensor products univariate brushlet functions regard to this covering. show that systems form an unconditional for -spaces

This paper investigates the empirical evidence on the link between foreign direct investment and trade (export and import) in Turkey over the period from 1992:01 to 2008:04 by using the minimum LM unit root test for stationarity; Granger and Dolado-Lüthkepohl tests for causality. The test results based on the bi-variate VAR model indicate that there is no evidence of causality between foreign d...

Consider a random vector, and assume that a set of its moments information is known. Among all possible distributions obeying the given moments constraints, the envelope of the probability distribution functions is introduced in this paper as distributional robust probability function. We show that such a function is computable in the bi-variate case under some conditions. Connections to the ex...