We investigate how well the graph of a bilinear function b : [0, 1]n → R can be approximated by its McCormick relaxation. In particular, we are interested in the smallest number c such that the difference between the concave upper bounding and convex lower bounding functions obtained from the McCormick relaxation approach is at most c times the difference between the concave and convex envelope...

We study L (or Lr,∞) boundedness for bilinear translation-invariant operators with nonnegative kernels acting on functions on R. We prove that if such operators are bounded on some products of Lebesgue spaces, then their kernels must necessarily be integrable functions on R, while via a counterexample we show that the converse statement is not valid. We provide certain necessary and some suffic...

This article deals with the tracking control of periodic references in single-input single-output bilinear systems using a stable inversion-based approach. Assuming solvability of the exact tracking problem and asymptotic stability of the nominal error system, the study focuses on the output behavior when the control scheme uses a periodic approximation of the nominal feedforward input signal u...

We present simpler and improved constructions of unbounded attribute-based encryption (ABE) schemeswith constant-size public parameters under static assumptions in bilinear groups. Concretely, we obtain: – a simple and adaptively secure unbounded ABE scheme in composite-order groups, improving upon a previousconstruction of Lewko and Waters (Eurocrypt ’11) which only achieves selective ...

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l∞-norm, that is, by a...

We consider a piecewise continuous, piecewise monotone interval map and a weight of bounded variation, constant on homtervals and continuous at periodic points of the map. With these data we associate a sequence of weighted Milnor-Thurston kneading matrices, converging to a countable matrix with coeecients analytic functions. We show that the determinants of these matrices converge to the inver...

Attenuation correction of PET emission data using spatially correlated CT images is fast and precise yielding a noise-free attenuation map (μmap) in comparison with radionuclide transmission scanning (TX). However, it is essential to convert the linear attenuation coefficients obtained from CT scans to those corresponding to 511 keV. Several conversion strategies have been developed including s...

Monocular depth estimation is a hot research topic in autonomous car driving. Deep convolution neural networks (DCNN) comprising encoder and decoder with transfer learning are exploited the proposed work for monocular map of two-dimensional images. Extracted CNN features from initial stages later upsampled using sequence Bilinear UpSampling layers to reconstruct map. The forms feature extractio...

We consider a linear Schrödinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric eld (the control). We prove the exact controllability of this system, in any positive time, locally around the ground state. Similar results were proved for particular models [14, 15, 17], in non optimal spaces, in long time and the proof relied on the Nash-...