On boundedness of discrete multilinear singular integral operators

Let $m(\xi,\eta)$ be a measurable locally bounded function defined in $\mathbb R^2$. Let $1\leq p_1,q_1,p_2,q_2<\infty$ such that $p_i=1$ implies $q_i=\infty$. Let also $0<p_3,q_3<\infty$ and $1/p=1/p_1+1/p_2-1/p_3$. We prove the following transference result: the operator {\mathcal C}_m(f,g)(x)=\int_{\bbbr} \int_{\bbbr} \hat f(\xi) \hat g(\eta) m(\xi,\eta) e^{2\pi i x(\xi +\eta)}d\xi d\eta initially defined for integrable functions with compact Fourier support, extends to a bounded bilinear operator from L^{p_1,q_1}(\bbbr)\times L^{p_2,q_2}(\bbbr) into L^{p_3,q_3}(\bbbr) if and only if the family of operators {\mathcal D}_{\widetilde{m}_{t,p}} (a,b)(n) =t^{\frac{1}{p}}\int_{-\12}^{\12}\int_{-\12}^{\12}P(\xi) Q(\eta) m(t\xi,t\eta) e^{2\pi in(\xi +\eta)}d\xi d\eta initially defined for finite sequences a=(a_{k_{1}})_{k_{1}\in \bbbz}, b=(b_{k_{2}})_{k_{2}\in \bbbz}, where P(\xi)=\sum_{k_{1}\in \bbbz}a_{k_{1}}e^{-2\pi i k_{1}\xi} and Q(\eta)=\sum_{k_{2}\in \bbbz}b_{k_{2}}e^{-2\pi i k_{2}\eta}, extend to bounded bilinear operators from l^{p_1,q_1}(\bbbz)\times l^{p_2,q_2}(\bbbz) into l^{p_3,q_3}(\bbbz) with norm bounded by uniform constant for all $t>0

Epistemological Beliefs and Knowledge among Physicians: A Questionnaire Survey

Background: All sciences share a common underlying epistemological domain, which gives grounds to and characterizes their nature and actions. Insofar as physicians depend on scientific knowledge, it would be helpful to assess their knowledge regarding some theoretical foundations of science. Objectives: 1.To assess resident physicians' knowledge of concepts and principles underlying all sciences. 2. To determine, to what extent physicians' epistemological beliefs and attitudes are compatible with the scientific paradigm. Design: A questionnaire was administered to 161 resident physicians at three hospitals in Lima, Peru. Results: 237 resident physicians were selected, 161 (68%) of whom agreed to answer the survey. 67% of respondents indicated they did not know what epistemology is, 21% were able to correctly define epistemology; 24% of the residents knew the appropriate definition of scientific theory. No respondents knew the philosophical presumptions of science; and 48% took a relativistic stand towards knowledge. Conclusions: There appear to be deficiencies in the knowledge of scientific theoretical foundations among physicians

Solutions of the Navier–Stokes Equation at Large Reynolds Number

The problem of two-dimensional incompressible laminar flow past a bluff body at large Reynolds number (R) is discussed. The governing equations are the Navier-Stokes equations. For R = ∞, the Euler equations are obtained. A solution for R large should be obtained by a perturbation of an Euler solution. However, for given boundary conditions, the Euler solution is not unique. The solution to be perturbed is the relevant Euler solution, namely the one which is the Euler limit of the Navier-Stokes solution with the same boundary conditions. For certain semi-infinite or streamlined bodies, the relevant Euler solution represents potential flow. For flow inside a closed domain a theorem of Prandtl states the relevant Euler solution has constant vorticity in each vortex. In many cases it can be determined by simultaneously considering the boundary layer equations. For flow past a bluff body, the relevant Euler solution is not known, although the free streamline flow for which the free streamline detaches smoothly from the body is a likely candidate. Even if this is correct, many unsolved problems remain. Various scalings have to be used for various regions of the flow. Possibilities of scaling for the various regions are discussed here. Special attention is paid to the region near the point of separation. A famous paper by Goldstein asserts that for an adverse smooth pressure gradient, the solution of the boundary layer equations can, in general, not be continued beyond the point of separation. Subsequent attempts by many authors to overcome the difficulty of continuation have failed. A very promising theory, going beyond conventional boundary layer theory, has recently been put forward independently by Sychev and Messiter. They assume that separation takes place in a sublayer whose thickness and length tend to zero as R tends to infinity. The pressure gradient in the sublayer is self-induced and is positive upstream of the point of separation and zero downstream. Their theory does not contradict experiments and numerical calculations, which may be reliable up to, say, R = 100, but it also shows that in this context, 100 may not be regarded as a large Reynolds number. The sublayer has the same scaling in orders of R as the sublayer at the trailing edge of a plate, found earlier by Stewartson and Messiter in studying the matching of the boundary layer solution on the plate with the Goldstein wake solution downstream of the trailing edge

Exact balanced random imputation for sample survey data

Surveys usually suffer from non-response, which decreases the effective sample size. Item non-response is typically handled by means of some form of random imputation if we wish to preserve the distribution of the imputed variable. This leads to an increased variability due to the imputation variance, and several approaches have been proposed for reducing this variability. Balanced imputation consists in selecting residuals at random at the imputation stage, in such a way that the imputation variance of the estimated total is eliminated or at least significantly reduced. In this work, we propose an implementation of balanced random imputation which enables to fully eliminate the imputation variance. Following the approach in Cardot et al. (2013), we consider a regularized imputed estimator of a total and of a distribution function, and we prove that they are consistent under the proposed imputation method. Some simulation results support our findings

On some spectral properties of TanDEM-X interferograms over forested areas

This letter reports about some obervations over rainforest (in Brazil and Indonesia), where the spectra of TanDEM-X interferograms show distinct features, almost a signature, which is explained and modelled in terms of the scattering properties. Supported by comparisons with simulations, the observations exclude any homogeneous, horizontally-layered forest; instead, they are compatible with a model with point scatterers clustered in clouds. Such a model, with high extinction and large gaps that allow significant penetration, is able to explain to a good degree the observations

SIGNAL: A Ka-band Digital Beam-Forming SAR System Concept to Monitor Topography Variations of Ice Caps and Glaciers

This paper discusses the implementation of an endto- end simulator for the BIOMASS mission. An overview of the system architecture is provided along with a functional description of the modules that comprise the simulator