In this paper we will study certain models of irreducible admissible representations of the split special orthogonal group SO(2n + 1) over a nonarchimedean local field. If n = 1, these models were considered by Waldspurger [Wa1,Wa2], and arose in his profound studies of the Shimura correspondence. If n = 2, they were considered by Novodvorsky and Piatetski-Shapiro [NP], who called them Bessel models, and for general n they were studied by Novodvorsky [No]. In the works cited, these authors established the uniqueness of these models; in this paper we establish functional equations and explicit formulas for them. In general, these models arise from a variety of RankinSelberg integrals (for example, those of Andrianov [An], Furusawa [Fu1], and Sugano [Su]), and the results of this paper will naturally have applications to the study of Lfunctions. Moreover, these models arise in the study of the theta correspondence between SO(2n + 1) and the double cover of Sp(2n), and they will therefore be of importance in generalizing the work of Waldspurger (see Furusawa [Fu2]).In the final Section, we present a global application of the explicit formulas: we consider the Eisenstein series (6.1) on SO(2n + 1) formed with a cuspidal automorphic representation π on GL(n), and we show that its Bessel period (6.2) is essentially a product of L-series L n(s − 1/2) + 1/2, π L n(s − 1/2) + 1/2, π ⊗ η ,
We evaluated the therapeutic effect of transcatheter arterial embolization therapy (TAE) for painful osseous metastases from hepatocellular carcinoma (HCC) in comparison with radiation therapy (RT). TAE using gelatin sponge particles was performed for seven lesions in seven patients. Selective catheterization and embolization were successfully performed in all lesions. Within 10 days after TAE, complete pain relief (CR), partial relief (PR) and no relief (NR) were attained in 57%, 29% and 14%, respectively. RT was used to treat 34 lesions in 22 patients. The dose fractionation schedules were in the range 28.0-50.4 Gy, with 1.8-4.0 Gy per fraction. CR, PR and NR were attained in 47%, 47% and 6%, respectively. There were no serious complications related to these treatments. Both TAE and RT are effective and the treatment of choice should be selected on an individual basis.
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