Weakly integrable semigroups on locally convex spaces

AbstractA class of weakly integrable semigroups on locally convex spaces is introduced and studied. The results are illustrated by examples of semigroups of unbounded operators on a Banach space, which include fractional powers of a closed operator and spectral local semigroups

Topological QFT

An earlier paper gave a means of calculating the Lamb shift via Feynman diagrams. Here we apply the same techniques to TQFT.Comment: arXiv admin note: substantial text overlap with arXiv:2204.0725

Holomorphic functions on the lie ball and their monogenic counterparts

The Cauchy integral formula in Clifford analysis allows us to associate a holomorphic function \tilde f:L_n\to \C on the Lie ball $L_n$ in \C^n with its monogenic counterpart f:B_1(0)\to \C^{n+1} via the formula \tilde f(z) = \int_{S^n}G_\om(z)\bs n(\om)f(\om)\,d\mu(\om), $z\in L_n.$ The inverse map $\tilde f\mapsto f$ is constructed here using the Cauchy-Hua formula for the Lie ball following the work of M. Morimoto \cite{Mori2}

Semivariation in LpL^p-spaces

summary:Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X\hat\otimes_\tau Y$ is their complete tensor product with respect to some tensor product topology $\tau$. A uniformly bounded $X$-valued function need not be integrable in $X\hat\otimes_\tau Y$ with respect to a $Y$-valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $\tau$ is the Hilbert space tensor product topology, in which case Grothendieck's theorem may be applied. In this paper, we take an index $1 \le p < \infty$ and suppose that $X$ and $Y$ are $L^p$-spaces with $\tau_p$ the associated $L^p$-tensor product topology. An application of Orlicz's lemma shows that not all uniformly bounded $X$-valued functions are integrable in $X\hat\otimes_{\tau_p} Y$ with respect to a $Y$-valued measure in the case $1\le p < 2$. For $2 < p <\infty$, the negative result is equivalent to the fact that not all continuous linear maps from $\ell^1$ to $\ell^p$ are $p$-summing, which follows from a result of S. Kwapien

Lp-valued measures without finite X-semivariation for 2 < p < ∞

We show that for 1 ≤ p < ∞, the property that every Lp-valued vector measure has finite X-semivariation in Lp(μ, X) is equivalent to the property that every continuous linear map from 1 to X is p-summing. For 2 < p < ∞, we explicitly construct an Lp([0, 1])-valued measure without finite Lp-semivariation.Generalitat ValencianaMinisterio de Educación y CienciaUniversidad Politécnica de ValenciaCentre for Mathematics and its Applications at the Australian National Universit

Viability of a Reusable In-Space Transportation System

The National Aeronautics and Space Administration (NASA) is currently developing options for an Evolvable Mars Campaign (EMC) that expands human presence from Low Earth Orbit (LEO) into the solar system and to the surface of Mars. The Hybrid in-space transportation architecture is one option being investigated within the EMC. The architecture enables return of the entire in-space propulsion stage and habitat to cis-lunar space after a round trip to Mars. This concept of operations opens the door for a fully reusable Mars transportation system from cis-lunar space to a Mars parking orbit and back. This paper explores the reuse of in-space transportation systems, with a focus on the propulsion systems. It begins by examining why reusability should be pursued and defines reusability in space-flight context. A range of functions and enablers associated with preparing a system for reuse are identified and a vision for reusability is proposed that can be advanced and implemented as new capabilities are developed. Following this, past reusable spacecraft and servicing capabilities, as well as those currently in development are discussed. Using the Hybrid transportation architecture as an example, an assessment of the degree of reusability that can be incorporated into the architecture with current capabilities is provided and areas for development are identified that will enable greater levels of reuse in the future. Implications and implementation challenges specific to the architecture are also presented

Are happy drivers safer drivers? Evidence from hazard response times and eye tracking data

Previous research shows that negative emotions have a detrimental effect on cognitive processes in general and on driving safety in particular. However to date, there has been no empirical investigation of the impact that positive emotions might have on driving safety. This research examined the influence of mood on driving safety using hazard perception videos and an eye tracker. Participants’ mood was manipulated (Sad, Neutral, Happy) after which they observed videos containing a number of potential hazards. Hazard response times and eye fixations were measured. The Sad mood affected drivers the most, with the longest response times and fixation durations. The effects of the Happy mood were less clear, suggesting that apart from emotional valence, emotional arousal should be considered. In addition, hazard response times differed as a function of hazard onset (i.e. unexpected or developing hazard) and type of hazard (i.e. human, car). The results are interpreted in terms of theories of positive emotions and psychological arousal

Controlling the Response: Predictive Modeling of a Highly Central, Pathogen-Targeted Core Response Module in Macrophage Activation

We have investigated macrophage activation using computational analyses of a compendium of transcriptomic data covering responses to agonists of the TLR pathway, Salmonella infection, and manufactured amorphous silica nanoparticle exposure. We inferred regulatory relationship networks using this compendium and discovered that genes with high betweenness centrality, so-called bottlenecks, code for proteins targeted by pathogens. Furthermore, combining a novel set of bioinformatics tools, topological analysis with analysis of differentially expressed genes under the different stimuli, we identified a conserved core response module that is differentially expressed in response to all studied conditions. This module occupies a highly central position in the inferred network and is also enriched in genes preferentially targeted by pathogens. The module includes cytokines, interferon induced genes such as Ifit1 and 2, effectors of inflammation, Cox1 and Oas1 and Oasl2, and transcription factors including AP1, Egr1 and 2 and Mafb. Predictive modeling using a reverse-engineering approach reveals dynamic differences between the responses to each stimulus and predicts the regulatory influences directing this module. We speculate that this module may be an early checkpoint for progression to apoptosis and/or inflammation during macrophage activation