This work is devoted to the study of the initial boundary value problem for a general isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see [16]), which can be used as a phase transition model. We will prove the existence of local and global (under a condition of smallness on the initial data) strong solutions with discontinuous initial density where ln ρ0 belongs to...

Developmental changes in speech production introduce age-dependent spectral and temporal variability in the speech signal produced by children. Such variabilities pose challenges for robust automatic recognition of children’s speech. Through an analysis of age-related acoustic characteristics of children’s speech in the context of automatic speech recognition (ASR), effects such as frequency sc...

Multi-channel sparse blind deconvolution, or convolutional coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This finds numerous applications in signal processing, computer vision, and inverse problems. However, it is challenging learn efficiently due bilinear structure observations respect inputs, as...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...

L p estimates for non smooth bilinear Littlewood-Paley square functions on R. Abstract In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. Mainly we prove boundedness-properties in Lebesgue spaces for them. Let us consider the function φn satisfying c φn(ξ) = 1 [n,n+1] (ξ) and consider the bilinear operator Sn(f, g)(x) := R ...

Bilinear operators are investigated in the context of Sobolev spaces and various techniques useful in the study of their boundedness properties are developed. In particular, several classes of symbols for bilinear operators beyond the so called CoifmanMeyer class are considered. Some of the Sobolev space estimates obtained apply to both the bilinear Hilbert transform and its singular multiplier...

At Eurocrypt 2010, Freeman proposed a transformation from pairing-based schemes in composite-order bilinear groups to equivalent ones in prime-order bilinear groups. His transformation can be applied to pairing-based cryptosystems exploiting only one of two properties of composite-order bilinear groups: cancelling and projecting. At Asiacrypt 2010, Meiklejohn, Shacham, and Freeman showed that p...

In this paper we present a finite dimensional iterative algorithm for optimal maximum a posteriori (MAP) state estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. We show that several bilinear models previously considered in the literature are special cases of the general bilinear model we propose. Our it...

f(x, y) = a x + x Qy + b y, where a, x ∈ R, b, y ∈ R, and Q is a matrix of dimension n ×m. It is easy to see that bilinear functions compose a subclass of quadratic functions. We refer to optimization problems with bilinear objective and/or constraints as bilinear problems, and they can be viewed as a subclass of quadratic programming. Bilinear programming has various applications in constraine...