An easily verifiable proof of the Brouwer fixed point theorem

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.Comment: 4 page

A New Rearrangement and the Theorem of Hardy-Littlewood-Polya

Article信州大学工学部紀要 41: 1-22 (1976)departmental bulletin pape

On a Theorem Concerning Minimization Problems on a Network

Article信州大学工学部紀要 44: 11-14 (1978)departmental bulletin pape

An Elementary Proof of The 2-Dimensional Version of The Brouwer Fixed Point Theorem

We give an elementary proof of the 2-dimensional version of the Brouwer fixed point theorem. The proof can be extended to the n-dimensional version naturally. In our proof, we only use the Bolzano-Weierstrass theorem and the fact that an odd number plus an even number is odd

A unified origin for the 3D magnetism and superconductivity in Nax_xCoO2_2

We analyze the origin of the three dimensional (3D) magnetism observed in nonhydrated Na-rich Na$_x$CoO$_2$ within an itinerant spin picture using a 3D Hubbard model. The origin is identified as the 3D nesting between the inner and outer portions of the Fermi surface, which arise due to the local minimum structure of the $a_{1g}$ band at the $\Gamma$-A line. The calculated spin wave dispersion strikingly resembles the neutron scattering result. We argue that this 3D magnetism and the spin fluctuations responsible for superconductivity in the hydrated systems share essentially the same origin.Comment: 5pages, 6figure

Scaled dynamic loading tests on seismic isolation bearing excluding the contamination of friction and inertia forces

Conventional seismic isolation-bearing testing facilities require moving horizontal platens under high compression. However, these dynamic moving platens inevitably lead to the friction and inertial forces generated by large vertical loads and inertial forces due to the dynamic mass action of the moving platen, which eventually affects the accuracy of the measured force. To solve this problem, the authors have proposed a direct reaction force measurement system (horizontal-vertical separated type) that can exclude the contamination of friction and inertial forces. Measuring pure reaction forces without the contamination of friction forces and inertia is crucial for the reliability of test results. In this paper, prior to the construction of large-scale facility, reduced-size–mockup dynamic tests were conducted using the proposed measurement concept, and its validity and accuracy were discussed. Furthermore, this system was applied to hybrid simulation tests, and the significant improvement of the proposed measurement system was observed

Relationship between the Concentration of Cyanide Ion Detected in Carp and That in Environmental Water

The toxicity of cyanide solution to carp increased with a rise in temperature. The result that the concentration of cyanide ion in blood was higher than that in hepatopancreas and spleen，or digestive tract of carp exposed to 10 ppm cyanide ion solution for 5 hours suggested that the ambient cyanide might enter into the blood through the gill. However, the cyanide ion concentration in skin and muscle was higher than that in viscera of carp died in 10 ppm cyanide ion solution. It can therefore be concluded that a large amount of cyanide penetrated into the fish body surface. Cyanide ion was detectable from carp washed by running tap water for 24 hours after death in 5 ppm cyanide ion solution ， and also from carp exposed to 10 ppm cyanide ion solution for 70 minutes after death of suffocation

Two regulatory steps of ER-stress sensor Ire1 involving its cluster formation and interaction with unfolded proteins

Chaperone protein BiP binds to Ire1 and dissociates in response to endoplasmic reticulum (ER) stress. However, it remains unclear how the signal transducer Ire1 senses ER stress and is subsequently activated. The crystal structure of the core stress-sensing region (CSSR) of yeast Ire1 luminal domain led to the controversial suggestion that the molecule can bind to unfolded proteins. We demonstrate that, upon ER stress, Ire1 clusters and actually interacts with unfolded proteins. Ire1 mutations that affect these phenomena reveal that Ire1 is activated via two steps, both of which are ER stress regulated, albeit in different ways. In the first step, BiP dissociation from Ire1 leads to its cluster formation. In the second step, direct interaction of unfolded proteins with the CSSR orients the cytosolic effector domains of clustered Ire1 molecules