Gukov-Pei-Putrov-Vafa constructed q-series invariants called homological blocks in a physical way in order to categorify Witten-Reshetikhin-Turaev (WRT) invariants and conjectured that radial limits of homological blocks are WRT invariants. In this paper, we prove their conjecture for unimodular H-graphs. As a consequence, it turns out that the WRT invariants of H-graphs yield quantum modular forms of depth two and of weight one with the quantum set Q. In the course of the proof of our main theorem, we first write the invariants as finite sums of rational functions. We second carry out a systematic study of weighted Gauss sums in order to give new vanishing results for them. Combining these results, we finally prove that the above conjecture holds for H-graphs.

No abstract

This study analyzes the degree of change in AHP questionnaire results based on the difference in the examinee's knowledge of the evaluation object. First, the AHP questionnaire is administered three times to the identical examinees. For each administration, the system of providing information differs. The three systems for imparting information are ① a text description; ② a text description, a photograph and a map; ③ and a field inspection. The comparison of the questionnaire results showed that evaluation based on a text description and a photograph had almost the same value as the evaluation based on the field inspection.

No abstract