On quaternionic functional analysis

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real $C^*$-algebras respectively. We will also give a Riesz representation theorem for quaternion Hilbert spaces and will extend two results of Kulkarni (namely, we will give the full versions of the Gelfand-Naimark theorem and the Gelfand theorem for quaternion $B^*$-algebras). On our way to these results, we compare, clarify and unify the term "quaternion Hilbert spaces" in the literatures.Comment: to appear in the Mathematical Proceedings of the Cambridge Philosophical Societ

Warped Functional Analysis of Variance

This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude and time variability. The focus is on single-random-factor models but the approach can be easily generalized to more complex ANOVA models. The behavior of the estimators is studied by simulation, and an application to the analysis of growth curves of flour beetles is presented. Although the model assumes a smooth latent process behind the observed trajectories, smoothness of the observed data is not required; the method can be applied to the sparsely observed data that is often encountered in longitudinal studies

Functional Analysis on Bali Botanical Garden for Society

Bali Botanical Gardens as one of the government agencies that play a role in conservation, research, education, tourism, and environmental services, have a great responsibility for the conservation of biodiversity in Indonesia. Bali Botanical Gardens take website advantage of existing services to promote the service program in the field of conservation and environmental education as well as contributing to socialize about preserving the environment. Bali botanical gardens provide a variety of information with the submission that is easily understood by tourists who want to visit. Bali Botanical Gardens itself makes the website and facebook fan page as the promotion, reporting and socialize both in terms of reporting to support e-government and the most important is the focus in the field of environment, the conservation of nature, the introduction and utilization of research results and an introduction to the various types of Mountain crops to the public. In addition to the website and facebook fan page Bali Botanical Gardens also use TripAdvisor know the feedback from the community after a visit to the Bali Botanical Gardens

Generating functional analysis of CDMA detection dynamics

We investigate the detection dynamics of the parallel interference canceller (PIC) for code-division multiple-access (CDMA) multiuser detection, applied to a randomly spread, fully syncronous base-band uncoded CDMA channel model with additive white Gaussian noise (AWGN) under perfect power control in the large-system limit. It is known that the predictions of the density evolution (DE) can fairly explain the detection dynamics only in the case where the detection dynamics converge. At transients, though, the predictions of DE systematically deviate from computer simulation results. Furthermore, when the detection dynamics fail to convergence, the deviation of the predictions of DE from the results of numerical experiments becomes large. As an alternative, generating functional analysis (GFA) can take into account the effect of the Onsager reaction term exactly and does not need the Gaussian assumption of the local field. We present GFA to evaluate the detection dynamics of PIC for CDMA multiuser detection. The predictions of GFA exhibits good consistency with the computer simulation result for any condition, even if the dynamics fail to convergence.Comment: 14 pages, 3 figure