A q-analogue of Catalan Hankel determinants

In this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a q-analogue of Catalan numbers $C_{n}=\frac1{n+1}\binom{2n}{n}$, which is known as the moments of the little q-Jacobi polynomials. We also give several proofs of this q-analogue, in which we use lattice paths, the orthogonal polynomials, or the basic hypergeometric series. We also consider a q-analogue of Schr\"oder Hankel determinants, and give a new proof of Moztkin Hankel determinants using an addition formula for ${}_2F_{1}$.Comment: 17 page

上皮間葉転換阻害剤のハイスループットスクリーニングのための新規細胞アッセイ：上皮間葉転換を阻害する承認薬および治験薬の同定

京都大学新制・課程博士博士(医学)甲第24879号医博第5013号京都大学大学院医学研究科医学専攻(主査)教授 後藤 慎平, 教授 渡邊 直樹, 教授 平井 豊博学位規則第4条第1項該当Doctor of Medical ScienceKyoto UniversityDFA

Generalizations of Cauchy's Determinant and Schur's Pfaffian

We present several generalizations of Cauchy's determinant and Schur's Pfaffian by considering matrices whose entries involve some generalized Vandermonde determinants. Special cases of our formulae include previuos formulae due to S.Okada and T. Sundquist. As an application, we give a relation for the Littlewood--Richardson coefficients involving a rectangular partition.Comment: 26 page

Mathematical Model for The Transmission of Lymphatic Filariasis and Its Applications

We have constructed a stochastic transmission model for lymphatic filariasis caused by Wuchereria bancrofti, and have analyzed its prevalence using computer simulations. In Pondicherry, India, where Wuchereria bancrofti has been spreading, the Vector Control Research Centre has carried out an integrated vector control strategy against malaria and filariasis for five years (1981~1985) with good results reported. Our study was aimed at evaluating the effect of vector control in the context of Pondicherry, and in particular the continuous effect for the post-control period. In this paper, we have used the LYMFASIM model proposed by Plaisier et al., the carrying capacity model by Rochet and the population dynamics model by us. In the LYMFASIM model and the carrying capacity model, we have modified the quantities of parameters in order to fit the models to the parasitological, entomological and epidemiological data in Pondicherry. We have combined the improved LYMFASIM model with the other models. Through simulations of our combinated model, we have compared the prevalence rate in the human population as well as the mean number of L3-larvae in the mosquito population, with and without vector control. As a result, the simulations show that the prevalence rate would be restrained for a long time even if only a small continuous effect of the vector control remains in the post-control period. However, the mean number of L3-larvae would recovered within a short time comparatively. This is because of the differences in life spans between human and mosquito as well as the incubation periods between the adult worm in the human host and L3-larvae in the mosquito vector

Goodwill transfigures harassment : A prolegomena for socio-philosophical exploration on the gift and the violence in education

This paper pursues socio-philosophical approach for violence around education such as school bullying, child abuse and campus harassment. In the mainstream of French sociology, social violence tends to be connected directly with “the sacred” and its effect like Durkheim and former Mauss. But after the death of Durkheim, Mauss suggested the ambivalence of gift between goodwill and poison on the “totality” of primitive society, which lead to theoretical roads both total symbolic interactionism and general structuralism. Lévi-Strauss resolved it into monolithic general exchange, on the other hand Baudrillard and Clastre described primitive society in the aspect of genetics of elemental power and violence with some examples of counter-violence. Their perspectives regard the gift and its violence as the result of fundamental human interaction, which are brought about our feeling of indebtedness based on social desire for admission. Then, how can we justify any violence against the power? Derrida answered this question reading Benjamin’s criticism deconstructively, expressing Benjamin’s mythic violence as “violence against violence.” From the empirical point of view, we find mythic violence means the self-sacrifice of “accusation” against compulsory violence. That counter-violence has ontological foundation in materiality of the language, therefore we can avoid structural ignorance on the worst violence of silence