Operator-Valued Continuous Gabor Transforms over Non-unimodular Locally Compact Groups

In this article, we present the abstract harmonic analysis aspects of the operator-valued continuous Gabor transform (CGT) on second countable, non-unimodular, and type I locally compact groups. We show that the operator-valued continuous Gabor transform CGT satisfies a Plancherel formula and an inversion formula. As an example, we study these results on the continuous affine group

Square-integrability of multivariate metaplectic wave-packet representations

This paper presents a systematic study for harmonic analysis of metaplectic wave-packet representations on the Hilbert function space L2(Rd). The abstract notions of symplectic wave-packet groups and metaplectic wave-packet representations will be introduced. We then present an admissibility condition on closed subgroups of the real symplectic group Sp(Rd), which guarantees the square-integrability of the associated metaplectic wave-packet representation on L2(Rd)

Absolutely Convergent Fourier Series of Functions over Homogeneous Spaces of Compact Groups

This paper presents a systematic study for classical aspects of functions with absolutely convergent Fourier series over homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and μ be the normalized G-invariant measure over the left coset space G/H associated with Weil’s formula with respect to the probability measures of G and H. We introduce the abstract notion of functions with absolutely convergent Fourier series in the Banach function space L1(G/H,μ). We then present some analytic characterizations for the linear space consisting of functions with absolutely convergent Fourier series over the compact homogeneous space G/H

Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time

We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function

Internationalising high-tech SMEs: advancing a new perspective of open innovation

Choosing a foreign market entry strategy is known to be essential for firm internationalisation yet there is very little focus on the role, purpose, and value of open innovation for internationalising high-tech SMEs. A review of the international business, international entrepreneurship and international marketing literature combined with a bibliometric mapping of 2501 articles on firm internationalisation, suggests that research does not readily associate open innovation and the internationalisation of high-tech SMEs. This is regardless of open innovation's activities that can span over a firm's immediate geographical space. Thus, this study introduces new theoretical explanations and a midrange open innovation theory to advance open innovation as an alternative foreign market entry strategy especially for internationalising high-tech SMEs. This has theoretical and practical implications for academics, international business managers, and practitioners because it introduces an alternative internationalisation strategy for SMEs

Abstract Poisson summation formulas over homogeneous spaces of compact groups

This paper presents the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups. Let G be a compact group, H be a closed subgroup of G, and μ be the normalized G-invariant measure over the left coset space G / H associated to the Weil’s formula. We prove that the abstract Fourier transform over G / H satisfies a generalized version of the Poisson summation formula

Exponentiating in Pairing Groups

We study exponentiations in pairing groups for the most common security levels and show that, although the Weierstrass model is preferable for pairing computation, it can be worthwhile to map to alternative curve representations for the non-pairing group operations in protocols

Global reward state affects learning and activity in raphe nucleus and anterior insula in monkeys

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