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In this paper, we first introduce the notion of a random Orlicz function, and further present the conditional Orlicz space generated from a random normed module. Second, we prove the denseness of the Orlicz heart of a random normed module $E$ in $E$ with respect to the $(\varepsilon, \lambda)$-topology. Finally, based on the above work, we establish a dual representation theorem on the conditional Orlicz space generated from a random normed module, which extends and improves some known results., Comment: 11 pages

Bound states in the continuum (BIC) are trapped eigenmodes with infinite $Q$ factors that are confined in the system. In this work, we propose a simple design for engineering a Friedrich-Wintgen BIC through the interference between a symmetry protected BIC and a surface lattice mode in a dimerized dielectric metasurface. The meta-atoms are comprised a symmetric double bar dimer. Using incident angle tuning an avoided crossing between the symmetry protected BIC and surface lattice mode is observed. At a specific detuning, the lower energy resonance vanishes, resulting in the formation of a Friedrich-Wintgen BIC. Investigations using coupled mode theory elucidate the role of the damping rate and coupling strength in the formation of the Friedrich-Wintgen BIC in the dimerized bar metasurface. By tuning the spacing between the two bars, Friedrich-Wintgen BIC can be engineered with controlled energy and damping rate. It is shown that the damping rate of the coupled modes can be considerably suppressed in this system. We envision that these results will not only enhance the understanding of strongly coupled interactions in metasurfaces but also indicate new paths for actively and passively controlling metasurface resonators for photonic applications., Comment: 8 pages, 4 figures

In this paper, we first introduce $\mathbb{L}$-$\mu$-measurable functions and $\mathbb{L}$-Bochner integrable functions on a finite measure space $(S,\mathcal{F},\mu),$ and give an $\mathbb{L}$-valued analogue of the canonical $L^{p}(\Omega,\mathcal{F},\mu).$ Then we investigate the completeness of such an $\mathbb{L}$-valued analogue and propose the Radon-Nikod$\acute{y}$m property of $\mathbb{L}$-Banach spaces. Meanwhile, an example constructed in this paper shows that there do exist an $\mathbb{L}$-Banach space which fails to possess the Radon-Nikod$\acute{y}$m property. Finally, based on above work, we establish the dual representation theorem of $\mathbb{L}$-Bochner integrable function spaces, which extends and improves the corresponding classical result.

Aminoacetonitrile (AAN), also known as glycinenitrile, has been suggested as a possible precursor of glycine and adenine in the interstellar medium. Here we present the chemical modeling of AAN and its isomers in hot cores using the three-phase chemical model NAUTILUS with the addition of over 300 chemical reactions of the three AAN isomers and related species. Our models predicted a peak gas phase abundance of AAN reaching the order of 10-8, which is consistent with observation towards Sgr B2(N). Regarding the reaction pathways of AAN and its isomers, we found that AAN is primarily formed via free radical reactions on grain surfaces during the early evolutionary stages. Subsequently, it is thermally desorbed into the gas phase as the temperature rises and is then destroyed by positive ions and radicals in gas phase. The isomers of AAN are formed through the hydrogenation reaction of CH3NCN on the grain surface and via electron recombination reactions of ion C2H5N2+ in gas phase. We speculate that there is a possibility for NCCN and AAN to react with each other, eventually leading to the formation of adenine in hot cores. However, further investigation is required to understand the efficiency of grain surfaces in adenine formation, through theoretical calculations or laboratory experiments in future research., Comment: 15 pages,8 figures,5 tables,accepted for publication in MNRAS

Sulfur chemistry in the formation process of low-mass stars and planets remains poorly understood. The protoplanetary disks (PPDs) are the birthplace of planets and its distinctive environment provides an intriguing platform for investigating models of sulfur chemistry. We analyzed the ALMA observations of CS 7-6 transitions in the HD 163296 disk and perform astrochemical modeling to explore its sulfur chemistry. We simulated the distribution of sulfur-containing molecules and compared it with observationally deduced fractional column densities. We have found that the simulated column density of CS is consistent with the observationally deduced fractional column densities, while the simulated column density of C$_2$S is lower than the observationally deduced upper limits on column densities. This results indicate that we have a good understanding of the chemical properties of CS and C$_2$S in the disk. We also investigated the influence of the C/O ratio on sulfur-containing molecules and found that the column densities of SO, SO$_2$, and H$_2$S near the central star are dependent on the C/O ratio. Additionally, we found that the $N$[CS]/$N$[SO] ratio can serve as a promising indicator of the disk's C/O ratio in the HD 163296. Overall, the disk of HD 163296 provides a favorable environment for the detection of sulfur-containing molecules., Comment: 16 pages, 7 figures