In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de Leeuw’s theorem for bilinear multipliers of strong and weak type. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding b...

The paper presents an algebraic characterization of observability and span-reachability of bilinear hybrid systems without guards, i.e. hybrid systems whose continuous dynamics is determined by bilinear control systems, and whose discrete transitions are triggered externally. The proposed characterization provides necessary and sufficient conditions for observability and spanreachability in ter...

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...

The bilinear map whose domain and range are identical is called self-bilinear map. Once such kind of bilinear map exists, the multilinear map can be constructed easily by using self bilinear map as a component. Yamakawa et al. have introduced the first secure self-bilinear map with auxiliary information based on the integer factoring assumption in Crypto 2014. Inspired by their work, we find th...

Previous work on unsupervised learning has shown that it is possible to learn Gabor-like feature representations, similar to those employed in the primary visual cortex, from the statistics of natural images. However, such representations are still not readily suited for object recognition or other high-level visual tasks because they can change drastically as the image changes to due object mo...

Hermite spectral methods are investigated for linear diffusion equations and the viscous Burgers’ equation in unbounded domains. When the solution domain is unbounded, the diffusion operator no longer has a compact resolvent, which makes the Hermite spectral methods unstable. To overcome this difficulty, a time-dependent scaling factor is employed in the Hermite expansions, which yields a posit...

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some s...

This paper contains a tutorial introduction to the ideas of geometric algebra, concentrating on its physical applications. We show how the definition of a ‘geometric product’ of vectors in 2and 3-dimensional space provides precise geometrical interpretations of the imaginary numbers often used in conventional methods. Reflections and rotations are analysed in terms of bilinear spinor transforma...

We prove the periodicity of all H-local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects ...

LetHN be the set of all N×N (complex) Hermitian matrices, and let trA = ∑N i=1 aii denotes the trace of a square matrix A = (aij) N i,j=1. HN is a real Hilbert space of dimension N with respect to the symmetric bilinear form (A,B) 7→ trAB. Let lN denotes the unique Lebesgue measure on HN which satisfies the relation lN(Q) = 1 for every cube Q ⊂ HN with edges of length 1. A Gaussian probability ...