Complex spherical codes with two inner products

A finite set $X$ in a complex sphere is called a complex spherical $2$-code if the number of inner products between two distinct vectors in $X$ is equal to $2$. In this paper, we characterize the tight complex spherical $2$-codes by doubly regular tournaments, or skew Hadamard matrices. We also give certain maximal 2-codes relating to skew-symmetric $D$-optimal designs. To prove them, we show the smallest embedding dimension of a tournament into a complex sphere by the multiplicity of the smallest or second-smallest eigenvalue of the Seidel matrix.Comment: 10 pages, to appear in European Journal of Combinatoric

Complex spherical codes with three inner products

Let $X$ be a finite set in a complex sphere of $d$ dimension. Let $D(X)$ be the set of usual inner products of two distinct vectors in $X$. A set $X$ is called a complex spherical $s$-code if the cardinality of $D(X)$ is $s$ and $D(X)$ contains an imaginary number. We would like to classify the largest possible $s$-codes for given dimension $d$. In this paper, we consider the problem for the case $s=3$. Roy and Suda (2014) gave a certain upper bound for the cardinalities of $3$-codes. A $3$-code $X$ is said to be tight if $X$ attains the bound. We show that there exists no tight $3$-code except for dimensions $1$, $2$. Moreover we make an algorithm to classify the largest $3$-codes by considering representations of oriented graphs. By this algorithm, the largest $3$-codes are classified for dimensions $1$, $2$, $3$ with a current computer.Comment: 26 pages, no figur

A characterization of skew Hadamard matrices and doubly regular tournaments

We give a new characterization of skew Hadamard matrices of size $n$ in terms of the data of the spectra of tournaments of size $n-2$.Comment: 9 page

Critical Behavior in Doping-Driven Metal−-Insulator Transition on Single-Crystalline Organic Mott-FET

We present the carrier transport properties in the vicinity of a doping-driven Mott transition observed at a field-effect transistor (FET) channel using a single crystal of the typical two-dimensional organic Mott insulator $\kappa$-(BEDT-TTF)$_2$CuN(CN)$_2$Cl ($\kappa$-Cl).The FET shows a continuous metal$-$insulator transition (MIT) as electrostatic doping proceeds. The phase transition appears to involve two-step crossovers, one in Hall measurement and the other in conductivity measurement. The crossover in conductivity occurs around the conductance quantum $e^2/h$ , and hence is not associated with "bad metal" behavior, which is in stark contrast to the MIT in half-filled organic Mott insulators or that in doped inorganic Mott insulators. Through in-depth scaling analysis of the conductivity, it is found that the above carrier transport properties in the vicinity of the MIT can be described by a high-temperature Mott quantum critical crossover, which is theoretically argued to be a ubiquitous feature of various types of Mott transitions. [This document is the unedited Authors' version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright \copyright American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/acs.nanolett.6b03817]Comment: 40 pages, 16 figures in Nano Letters, ASAP (2017

EOSDB: The Database for Nuclear EoS

Nuclear equation of state (EoS) plays an important role in understanding the formation of compact objects such as neutron stars and black holes. The true nature of the EoS has been a matter of debate at any density range not only in the nuclear physics but also in the astronomy and astrophysics. We have constructed a database of EoSs by compiling data from the literature. Our database contains the basic properties of the nuclear EoS of symmetric nuclear matter and of pure neutron matter. It also includes the detailed information about the theoretical models, for example the adopted methods and assumptions in individual models. The novelty of the database is to consider new experimental probes such as the symmetry energy, its slope relative to the baryon density, and the incompressibility, which enables the users to check their model dependences. We demonstrate the performance of the EOSDB through the examinations of the model dependence among different nuclear EoSs. It is reveled that some theoretical EoSs, which is commonly used in astrophysics, do not satisfactorily agree with the experimental constraints.Comment: 30 pages, 5 figures, submitted to Publications of the Astronomical Society of Japan (revised

Research on indoor environment purification using charged droplet via electrospray method

広島大学(Hiroshima University)博士(工学)Doctor of Engineeringdoctora

軸不斉配位子を利用するアキラルなメタクリル酸エステルの高選択的不斉アニオン重合

金沢大学工学部不斉要素のない, 嵩高いエステル基を持つメタクリル酸モノマーの不斉アニオン重合に於けるコンホメーション規制に, 極めて高い立体選択性を示す重合触媒の構築に成功した. 即ち光学活性なビフェニル, ビナフチル, 或は酒石酸から誘導されるC2キラルな置換基で修飾したテトラメチルエチレンジアミン(TMEDA)誘導体を新規合成した. これらの不斉配位子と種々の有機リチウム化合物を組み合わせた触媒を用いて, メタクリル酸トリフェニルメチル(TrMA)をトルエン中, -78°Cで重合すると高い施光度を示すポリマーが得られる. ポリマーの施光度は用いた配位子の構造に強く依存する. 配位子の不斉な置換基としては, 不斉炭素による酒石酸誘導体より軸不斉を有するアビリルのほうが高い選択性を示す. 片側のジメチルアミノ基だけにキラルな置換基を導入したTMEDA誘導体と, その両側置換体とでは逆の立体選択性を示す. これらの一見複雑な結果も対カチオンに配位した不斉配位子に対して成長末端カルバニオンが採る熱力学的により安定な立体配置を考えると説明でき, 配位子のC2キラリティーと優先するポリマーのヘリシティーとの間には単一の立体化学的な関係が成立していた. ビフェニル片側置換体はTrMAばかりでなく, その2-ビリジル誘導体の重合の何れでも高い立体選択性を示す. 定量的に得られたこれらのポリマーはほぼ完全に一方巻の螺旋構造を有し, 且つ有機溶剤に溶け得る程度の適度な重合度になる. また, 配位子の立体配置を変えて得られる+と-のポリマーは互いに鏡像体である. しかし嵩高くないメタクリル酸メチル, ベンジルを重合しても有意な施光性を示すポリマーは得られないことから, これらのイソタクトポリマーが溶液中で螺旋構造をとる可能性について我々は現時点で否定的な見解を持っている. 上記のポリマーのうち溶媒可溶で光学活性なものからは高効率な光学分割用HPLCのキラル充填剤を調製することができた.The asymmetric polymerization of achiral methacrylates having bulky ester groups was achieved successfully by using the following chiral anionic initiators. Thus, we synthesized optically active tetramethylethylenediamine (TMEDA) derivatives modified with C_2-chiral substituents derived from tartaric acid having asymmetric carbons, or more preferentially from atropisomeric biphenyls and binaphthyls. These ligands were complexed effectively to various organolithium compounds. The resulting chiral complexes polymerized triphenylmethyl methacrylate (TrMA) in toluene at -78゜C. The produced polymers showed high optical rotations owing to the helical conformation, which was formed with high stereosectivity through the polymerization. The rotation values and senses of the polymers were strongly depending upon the structures of the used ligands. Although reaher complicated stereochemical product/ligand correlations were observed, they were consistently explained in terms of the stereoelectronic interaction between the propagating end of the polymer chain and the chiral ligand complexed to the counter lithium cation. One of the most effective ligands was a biphenyl-monosubstituted TMEDA. Its lithium complexes served as effective initiators for the polymerization of not only TrMA but also its 2- pyridyl derivative. The polymers produced quantitatively had almost pure one-handed heliciy, and have so limited molecular weights as to be easily soluble in tetrahydrofuran. The optically active and solvent-soluble polymers were useful as chiral packing materials for HPLC. On the other hand, when less bulky methacrylates of methyl and benzyl alcohols were polymerized with the above initiators, the produced isotactic polymers showed negligible rotations. From this result, we now consider that such poly(ester)s can\u27t form helical conformation being enough stable in solutions.研究課題/領域番号:61470105, 研究期間(年度):1986 – 1987出典：研究課題「軸不斉配位子を利用するアキラルなメタクリル酸エステルの高選択的不斉アニオン重合」課題番号61470105（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/ja/report/KAKENHI-PROJECT-61470105/614701051987kenkyu_seika_hokoku_gaiyo/）を加工して作

光学活性イオン交換樹脂の合成とラセミ化合物の分割

金沢大学工学部研究課題/領域番号:X43120-----59058, 研究期間(年度):1968出典：研究課題「光学活性イオン交換樹脂の合成とラセミ化合物の分割」課題番号 X43120-----59058（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） （https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-X43120-----59058/）を加工して作

Measurement of core-shifts with astrometric multi-frequency calibration

VLBI is unique, among the space geodetic techniques, in its contribution to defining and maintaining the International Celestial Reference Frame, providing precise measurements of coordinates of extragalactic radiosources. The quest for increasing accuracy of VLBI geodetic products has lead to a deeper revision of all aspects that might introduce errors in the analysis. The departure of the observed sources from perfect, stable, compact and achromatic celestial targets falls within this category. This paper is concerned with the impact of unaccounted frequency-dependent position shifts of source cores in the analysis of dual-band S/X VLBI geodesy observations, and proposes a new method to measure them. The multi-frequency phase transfer technique developed and demonstrated by Middelberg et al. (2005) increases the high frequency coherence times of VLBI observations, using the observations at a lower frequency. Our proposed SOURCE/FREQUENCY PHASE REFERENCING method endows it with astrometric applications by adding a strategy to estimate the ionospheric contributions. Here we report on the first successful application to measure the core shift of the quasar 1038+528 A at S and X-bands, and validate the results by comparison with those from standard phase referencing techniques. In this particular case, and in general in the cm-wavelength regime, both methods are equivalent. Moreover the proposed method opens a new horizon with targets and fields suitable for high precision astrometric studies with VLBI, especially at high frequencies where severe limitations imposed by the rapid fluctuations in the troposphere prevent the use of standard phase referencing techniques.Comment: 6 pages, 2 figures. Proceedings of 17th Working Meeting on European VLBI for Geodesy and Astrometry (April 2005