This paper mainly concerns the essential normality of graded submodules. Essentially all of the basic Hilbert modules that have received attention over the years are p-essentially normal-including the d-shift Hilbert module, the Hardy and Bergman modules of the unit ball. Arveson conjectured graded submodules over the unit ball inherit this property and provided motivations to seek an affirmative answer. Some positive results have been obtained by Arveson and Douglas. However, the problem has been resistant. In dimensions d = 2, 3, this paper shows that the Arveson's conjecture is true. In any dimension, the paper also gives an affirmative answer in the case of the graded principal submodule. Finally, the paper is associated with K -homology invariants arising from graded quotient modules, by which geometry of the quotient modules and geometry of algebraic varieties are connected. In dimensions d = 2, 3, it is shown that K -homology invariants determined by graded quotients are nontrivial. The paper also establishes results on p-smoothness of K -homology elements, and gives an explicit expression for K -homology invariant in dimension d = 2.
Nitrogen‐rich 3, 4‐bis(1H‐tetrazol‐5‐yl)furoxan (H2BTF, 2) and its energetic salts with excellent thermal stability were successfully synthesized and fully characterized by 1H, and 13C NMR, and IR spectroscopy, differential scanning calorimetry (DSC), and elemental analyses. Additionally, the structures of barium (3) and 1‐methyl‐3, 4, 5‐triamino‐triazolium (10) salts were confirmed by single‐crystal X‐ray diffraction. The densities of the energetic salts paired with organic cations range between 1.56 and 1.85 g·cm–3 as measured by a gas pycnometer. Based on the measured densities and calculated heats of formation, the detonation pressures and velocities are calculated to be in the range 23.4–32.0 GPa and 7939–8915 m·s–1, which make them competitive energetic materials.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.