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This paper is concerned with the Helmholtz decomposition of vector fields on bounded domains and exterior domains, and provides the decompositions in Sobolev spaces and Besov spaces of order in certain interval. In particular, the decompositions in homogeneous Besov spaces $\dot{B}_{1,q}^{s}$ and $\dot{B}_{\infty,q}^{s}$ are given.

A novel molecule, TatBim-Alexa, consisting of the HIV1 Tat cell-penetrating peptide, the Bim apoptosis-inducing peptide, and Alexa Fluor 546 was synthesized for photoinducion of apoptosis. The Alexa Fluor 546 was used as a photosensitizer and covalently attached at the C-terminus of TatBim peptide by the thiol-maleimide reaction. Photo-dependent cytosolic internalization of TatBim-Alexa and photo-dependent apoptosis using TatBim-Alexa were demonstrated in several kinds of mammalian cells including human cancer cell lines.

A multicore system-on-chip (SoC) has been developed for various applications (recognition, inference, measurement, control, and security) that require high-performance processing and low power consumption. This SoC integrates three types of synthesizable processors: eight CPUs (M32R), two multi-bank matrix processors (MBMX), and a controller (M32C). These processors operate at 1 GHz, 500 MHz, and 500 MHz, respectively. These three types of processors are interconnected on this chip with a high-bandwidth multi-layer system bus. The eight CPUs are connected to a common pipelined bus using a cache coherence mechanism. Additionally, a 512-kB L2 cache memory is shared by the eight CPUs to reduce internal bus traffic. A multi-bank matrix processor with 2-read/1-write calculation and background I/O operation has been adopted. The 1-GHz CPU is realized using a delay management network which consists of delay monitors that can be applied for any kind of application or process technology. Our configurable heterogeneous architecture with nine CPUs and two matrix processors reduces power consumption by 45%.