An efficient algorithm for finding all solutions of separable systems of nonlinear equations

An efficient algorithm is proposed for finding all solutions of systems of nonlinear equations with separable mappings. This algorithm is based on interval analysis, the dual simplex method, the contraction method, and a special technique which makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a system of 2000 nonlinear equations in acceptable computation time. AMS subject classification (2000)  65H10, 65G10     

Spin-dependent tunneling and Coulomb blockade in ferromagnetic nanoparticles

In this paper we review studies on spin-dependent transport in systems containing ferromagnetic nanoparticles. In a tunnel junction with a nanometer-scale-island, the charging effect leads to an electric current blockade phenomenon in which a single electron charge plays a significant role in electron transport, resulting in single-electron tunneling (SET) properties such as Coulomb blockade and Coulomb staircase. In a tunnel junction with a ferromagnetic nano-island and electrode, it was expected that the interplay of spin-dependent tunneling (SDT) and SET, i.e., spin-dependent single-electron tunneling (SD-SET), would give rise to remarkable tunnel magnetoresistance (TMR) phenomena. We investigated magnetotransport properties in both sequential tunneling and cotunneling regimes of SET and found the enhancement and oscillation of TMR. The self-assembled ferromagnetic nanoparticles we have employed in this study consisted of a Co–Al–O granular film with cobalt nanoparticles embedded in an Al–O insulating matrix. A _Co36Al22O42${\mathrm{Co}}_{36}{\mathrm{Al}}_{22}{\mathrm{O}}_{42}$ film prepared by a reactive sputtering method produced a TMR ratio reaching 10% and superparamagnetic behavior at room temperature. The TMR ratio exhibited an anomalous increase at low temperatures but no indication of change with bias voltage. In Section 4, we show that the anomalous increase of the MR provided evidence for higher-order tunneling (cotunneling) between large granules through intervening small granules. We emphasize that the existence of higher-order tunneling is a natural consequence of the granular structure, since broad distribution of granule size is an intrinsic property of granular systems. In Section 5, we concentrate on SD-SET properties in sequential tunneling regimes. We fabricated two types of device structures with Co–Al–O film using focused ion-beam milling or electron-beam lithography techniques. One had a granular nanobridge structure: point-shaped electrodes separated by a very narrow lateral gap filled with the Co–Al–O granular film. The other had a current-perpendicular-to-plane (CPP) geometry structure: a thin Co–Al–O granular film sandwiched by ferromagnetic electrodes with the current flowing in the direction perpendicular to the film plane through a few Co particles. We found the enhancement and oscillation of TMR due to spin-dependent SET in sequential tunneling regimes. In Section 6, we report experimental evidence of a spin accumulation effect in Co nanoparticles leading to the oscillation of TMR with alternate sign changes. Furthermore, we discovered that the spin relaxation time in the nanoparticles is unprecedentedly enhanced up to the order of more than hundreds of nanoseconds, compared to that evaluated from the spin-diffusion length of ferromagnetic layers in previous CPP-GMR studies, i.e., the order of tens of picoseconds.     

Beta-strand flipping and slipping triggered by turn replacement reveal the opportunistic nature of beta-strand pairing

We investigated how the register between adjacent beta-strands is specified using a series of mutants of the single-layer beta-sheet (SLB) in Borrelia OspA. The single-layer architecture of this system eliminates structural restraints imposed by a hydrophobic core, enabling us to address this question. A critical turn (turn 9/10) in the SLB was replaced with a segment with an intentional structural mismatch. Its crystal structure revealed a one-residue insertion into the central beta-strand (strand 9) of the SLB. This insertion triggered a surprisingly large-scale structural rearrangement: (i) the central strand (strand 9) was shifted by one residue, causing the strand to flip with respect to the adjacent beta-strands and thus completely disrupting the native side-chain contacts; (ii) the three-residue turn located on the opposite end of the beta-strand (turn 8/9) was pushed into its preceding beta-strand (strand 8); (iii) the register between strands 8 and 9 was shifted by three residues. Replacing the original sequence for turn 8/9 with a stronger turn motif restored the original strand register but still with a flipped beta-strand 9. The stability differences of these distinct structures were surprisingly small, consistent with an energy landscape where multiple low-energy states with different beta-sheet configurations exist. The observed conformations can be rationalized in terms of maximizing the number of backbone H-bonds. These results suggest that adjacent beta-strands "stick" through the use of factors that are not highly sequence specific and that beta-strands could slide back and forth relatively easily in the absence of external elements such as turns and tertiary packing.     

Nematic ordered cellulose templates mediating order-patterned deposition accompanied with synthesis of calcium phosphates

In a previous study, the nematic ordered cellulose (NOC) templates successfully induced biodirected epitaxial nanodeposition of cellulose nanofibers secreted by Gluconacetobacter xylinus along the orientation of the molecular tracks (Kondo et al. 2002). As an extended concept for the NOC, this article attempts to propose a sort of biomimic mineralization using the template. It combines morphologically controlling process with synthesis of the calcium phosphate as a major component of bones. This process was initially mediated by the modified NOC template having a pair of roles of the ion supply sources and scaffolds for 3D-ordering architecture of the calcium phosphate as a biomineral in the key functions for biomineralization. The successful establishment of such an ordered deposition of the inorganic on the template was confirmed by several surface characterizations such as atomic force microscopy, X-ray photoelectron spectroscopy, scanning electron microscopy, and so on. Moreover, similarly to human bones, the obtained major assemble states of the calcium phosphates exhibited amorphous. The above process using the bifunctional cellulose template can be considered as a biomimic mineralization, which also opens pathways toward preparation of potentially versatile organic–inorganic order-patterned composites under a less energy consumption.     

The shapes of critical loci of binary fluid mixtures on the p–T plane

The relations between the shapes of the critical loci of binary fluid mixtures and the positions of the critical points of their component fluids on the p–T plane were considered theoretically. The consideration was carried out for vapor–liquid phase equilibria in the model systems without liquid–liquid equilibria. We focused only the relations between the shapes and the tangent of the straight lines connecting the critical points of the component fluids on the p–T plane, and so the effects of the distance between the critical points were out of the scope of this work. The changes in the shapes of the critical loci were classified logically into three patterns. Literature survey has shown that the two patterns exist in the experimental results for several types of mixtures. The shapes of the critical loci of the binary fluid mixtures on the p–T plane are closely related to the relative positions between the critical points of their component fluids.     

Structure of securinine

The structure (XXVII) proposed for securinine is confirmed by synthetic structural proof of the key degradation products, lactam-carbinol B (XXIII) and quinolizidine B (XX).