Let $$F_{\infty }={{\mathbb {F}}_q}\left( \!\left( {1/T}\right) \!\right) $$ be the completion of $${\mathbb {F}}_q(T)$$ at 1/T. We develop a theory Fourier expansions for harmonic cochains on edges Bruhat–Tits building $${{\,\textrm{PGL}\,}}_r(F_{\infty })$$ , $$r\ge 2$$ generalizing an earlier construction Gekeler $$r=2$$ . then apply this to study modular units Drinfeld symmetric space $$\Om...

We combine recent developments on weakly symmetric pseudo--riemannian nilmanifolds with geometric methods for construction of unitary representations square integrable Dolbeault cohomology spaces. This runs parallel to discrete series spaces harmonic forms values in holomorphic vector bundles over flag domains. Some special cases had been described by Satake 1971 and the author 1975. Here we de...

Toshika Ohkawa,1,3 Shin’Ichiro Satake,2,3 Norihiko Yokoi,1,3 Yu Miyazaki,4 X Tomohiko Ohshita,5 Gen Sobue,4 Hiroshi Takashima,6 Osamu Watanabe,6 Yuko Fukata,1,3* and Masaki Fukata1,3* 1Division of Membrane Physiology, Department of Cell Physiology, and 2Division of Neural Signaling, Department of Information Physiology, National Institute for Physiological Sciences, National Institutes of Natur...

MICROCAPSULES USING MICRO-AIRFLOW-NOZZLE Shinji Sugiura, Tatsuya Oda, Yasuyuki Aoyagi, Ryota Matsuo, Tsuyoshi Enomoto, Kunio Matsumoto, Toshikazu Nakamura, Mitsuo Satake, Atsushi Ochiai, Nobuhiro Ohkohchi and Mitsutoshi Nakajima Research Center of Advanced Bionics, National Institute of Advanced Industrial Science and Technology (AIST), Central 5th, 1-1-1 Higashi, Tsukuba 305-8565, Japan Food E...

We show that the Hodge conjecture is false in general for products of surfaces. We construct a K3 surface whose transcendental lattice has a self-isomorphism which is not a linear combination of self-isomorphisms which preserve cup products over Q up to nonzero multiples. We then find another surface mapping into it in which the transcendental lattice is generated by H 1 cup products according ...

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces X “ G{K of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable G-invariant Finsler metric on X. As an application, we establish the existence of natural bordifications, as orbifolds-with-corners, of locally symmetric spaces X{Γ for arbitrary discrete subgroups ...

[1] Coastal stratigraphy of eastern Hokkaido indicates that decimeters of coastal uplift occurred repeatedly in the late Holocene. Employing radiocarbon dating and tephrochronology, we identify along a 100 km length of the Kuril subduction zone six uplift events since 2,800 years B.P. Uplift events occur at the same frequency as unusually high tsunamis. Each coastal uplift event, which occurs o...

Let G be a complex semisimple group and U its maximal unipotent subgroup. We study the algebra D(G/U) of algebraic differential operators on G/U also quasi-classical counterpart: regular functions T?(G/U), cotangent bundle. A long time ago, S. Gelfand M. Graev have constructed an action Weyl by automorphisms. The Gelfand-Graev construction was not algebraic, it involved analytic methods in esse...

electrocardiogram (ecg) is one of the most common biological signals which plays a significant role in diagnosis of heart diseases. one of the most important parts of ecg signal processing is interpretation of qrs complex and obtaining its characteristics. r wave is one of the most important sections of this complex which has an essential role in diagnosis of heart rhythm irregularities and als...