Unbiased orthogonal designs

The notion of unbiased orthogonal designs is introduced as a generalization of unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several methods of construction for mutually unbiased orthogonal designs. As an application, mutually quasi-unbiased weighing matrices for various parameters are obtained.     

Disjoint weighing matrices

Journal of Algebraic Combinatorics - The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search leads to...     

Contracted Representation of Yang's Spacetime Algebra and Buniy-Hsu-Zee's Discrete Spacetime

Motivated by the recent proposition by Buniy, Hsu, and Zee with respect to discrete spacetime and finite spatial degrees of freedom of our physical world with short- and long-distance scales, l _P and L, we reconsider the Lorentz-covariant Yang's quantized spacetime algebra (YSTA), which is intrinsically equipped with two such kinds of scale parameters, λ and R. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio R/λ, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, λ → 0 and R → ∓.     

Feasibility of carboxymethylcellulose with phenol moieties as a material for mammalian cell-enclosing subsieve-size capsules

Mammalian cell-enclosing capsules have been investigated as devices for bioproduction, cell therapy and stem cell research. In this study, carboxymethylcellulose (CMC) with phenol moieties (CMC-Ph), synthesized through the conjugation reaction of CMC and tyramine, was investigated as a material for these types of devices. Subsieve-size capsules of less than 100 μm in diameter were prepared by extruding aqueous CMC-Ph solution into co-flowing liquid paraffin containing H₂O₂. The capsule diameter was controlled between 60–220 μm by changing the flow rate of liquid paraffin. There was no harmful effect specific for CMC-Ph on mammalian cells enclosed in capsules. Feline kidney cells enclosed in subsieve-size CMC-Ph capsules exhibited 87.0 ± 4.5% viability. In addition, the enclosed cells continued to grow over 13 days of study. These results demonstrated the feasibility of CMC-Ph as a material for subsieve-size cell-enclosing capsules prepared via the droplet breakup technique in a co-flowing water-immiscible fluid.     

The influence of Cr content in Fe-Cr-Co alloys on the magnetic properties and Mössbauer effect

Fe-xCr-8Co (x=24, 25, 27, 29 and 32 wt%) permanent magnetic alloys have been studied bv Mössbauer effect, magnetic balance and vibrating-sample magnetometer. It is indicated that the optimum permanent magnetic properties obtained for the composition of the alloys at about x=27. The value of Cr content in these alloys sigificantly influences the average hyperfine field, the saturation magnetic moment, the proportion of paramagnetic phase and orientation of magnetic moment in these alloys. The intrinsic coercive force is gradually reduced with the temperature decreasing from 290 to 77k. The paramagnetic peak in the spectrum disappars at about 125k. The certain mechanism has been suggested to explain the experimental results.     

Microstructural analysis of La2/3 − xLi3xTiO3 single crystals and quenched samples observed by high resolution transmission electron microscopy

The La ordering and domain structures of La_2/3 ? xLi_3xTiO₃ single crystals and quenched samples have been observed by high resolution electron microscopy. In single crystals, the grown single crystals are not real single crystals with mono-domain, but crystals with 90° oriented domains with 20–100 nm sizes. A remarkable difference of the domain size between polycrystals and single crystals has not been observed at the same composition. In quenched samples, the La disordering has been observed. Furthermore, domain structures of quenched samples are different from those of furnace-cooled ones. Domain structures change with the La disordering. The understanding of microstructures is necessary to clarify the Li-ion conduction mechanism.     

Synthesis of 1-hydrocarbon substituted cyclopropyl silyl ketones

The synthesis of cyclopropyl silyl ketones possessing a hydrocarbon group at 1-position of three-membered ring was investigated. The reaction of sulfoxonium ylide with α,β-unsaturated acylsilanes derived from α,β-unsaturated aldehydes did not afford the desired acylsilane derivatives. Instead, the corresponding silyl enol ethers were yielded exclusively. On the other hand, the Corey-Chaykovsky cyclopropanation of α-substituted α,β-unsaturated aldehydes proceeded well to give 1-substituted cyclopropyl aldehydes. The silyl substitution of formyl proton in the obtained aldehydes via umpolung of carbonyl group afforded the target acylsilanes.     

A Direct S0→Tn Transition in the Photoreaction of Heavy-Atom-Containing Molecules

According to the Grotthuss–Draper law, light must be absorbed by a substrate to initiate a photoreaction. There have been several reports, however, on the promotion of photoreactions using hypervalent iodine during irradiation with light from a non-absorbing region. This contradiction gave rise to a mystery regarding photoreactions involving hypervalent iodine. We demonstrated that the photoactivation of hypervalent iodine with light from the apparently non-absorbing region proceeds via a direct S₀→T_n transition, which has been considered a forbidden process. Spectroscopic, computational, and synthetic experimental results support this conclusion. Moreover, the photoactivation mode could be extended to monovalent iodine and bromine, as well as bismuth(III)-containing molecules, providing new possibilities for studying photoreactions that involve heavy-atom-containing molecules.     

p-adic Siegel–Eisenstein series of degree two

We prove an explicit formula for Fourier coefficients of Siegel–Eisenstein series of degree two with a primitive character of any conductor. Moreover, we prove that there exists the p-adic analytic family which consists of Siegel–Eisenstein series of degree two and a certain p-adic limit of Siegel–Eisenstein series of degree two is actually a Siegel–Eisenstein series of degree two.