DD-optimal saturated designs: a simulation study

In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric structure of the design and we compare them with the classical $D$-efficiency criterion. We perform a simulation study. In all the test cases we observe that designs with high values of $D$-efficiency have also high values of the new objective functions.Comment: 8 pages. Preliminary version submitted to the 7th IWS Proceeding

Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.Comment: 25 pages, 5 figure

Koszul binomial edge ideals

It is shown that if the binomial edge ideal of a graph $G$ defines a Koszul algebra, then $G$ must be chordal and claw free. A converse of this statement is proved for a class of chordal and claw free graphs

Evidence for Strong-coupling S-wave Superconductivity in MgB2 :11B NMR Study

We have investigated a gap structure in a newly-discovered superconductor, MgB2 through the measurement of 11B nuclear spin-lattice relaxation rate, ^{11}(1/T_1). ^{11}(1/T_1) is proportional to the temperature (T) in the normal state, and decreases exponentially in the superconducting (SC) state, revealing a tiny coherence peak just below T_c. The T dependence of 1/T_1 in the SC state can be accounted for by an s-wave SC model with a large gap size of 2\Delta /k_BT_c \sim 5 which suggests to be in a strong-coupling regime.Comment: 2 pages with 1 figur

Multigap Superconductivity in Y2_2C3_3: A 13^{13}C-NMR Study

We report on the superconducting (SC) properties of Y$_2$C$_3$ with a relatively high transition temperature $T_{\rm c}=15.7$ K investigated by $^{13}$C nuclear-magnetic-resonance (NMR) measurements under a magnetic field. The $^{13}$C Knight shift has revealed a significant decrease below $T_{\rm c}$, suggesting a spin-singlet superconductivity. From an analysis of the temperature dependence of the nuclear spin-lattice relaxation rate $1/T_1$ in the SC state, Y$_2$C$_3$ is demonstrated to be a multigap superconductor that exhibits a large gap $2\Delta/k_{\rm B}T_{\rm c}=5$ at the main band and a small gap $2\Delta/k_{\rm B}T_{\rm c}=2$ at other bands. These results have revealed that Y$_2$C$_3$ is a unique multigap s-wave superconductor similar to MgB$_2$.Comment: 4 pages, 5 figure

Infrared/optical - X-ray simultaneous observations of X-ray flares in GRB 071112C and GRB 080506

We investigate the origin of short X-ray flares which are occasionally observed in early stages of afterglows of gamma-ray bursts (GRBs). We observed two events, GRB 071112C and GRB 080506, before the start of X-ray flares in the optical and near-infrared (NIR) bands with the 1.5-m Kanata telescope. In conjunction with published X-ray and optical data, we analyzed densely sampled light curves of the early afterglows and spectral energy distributions (SEDs) in the NIR-X-ray ranges. We found that the SEDs had a break between the optical and X-ray bands in the normal decay phases of both GRBs regardless of the model for the correction of the interstellar extinction in host galaxies of GRBs. In the X-ray flares, X-ray flux increased by 3 and 15 times in the case of GRB 071112C and 080506, respectively, and the X-ray spectra became harder than those in the normal decay phases. No significant variation in the optical-NIR range was detected together with the X-ray flares. These results suggest that the X-ray flares were associated with either late internal shocks or external shocks from two-component jets.Comment: 10 pages, 5 figures, accepted to Astronomy and Astrophysic

Toric rings, inseparability and rigidity

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of cotangent module $T^1(R)$ of $R$. In this article we focus on deformations of toric rings, and give an explicit description of $T^1(R)$ in the case that $R$ is a toric ring. In particular, we are interested in unobstructed deformations which preserve the toric structure. Such deformations we call separations. Toric rings which do not admit any separation are called inseparable. We apply the theory to the edge ring of a finite graph. The coordinate ring of a convex polyomino may be viewed as the edge ring of a special class of bipartite graphs. It is shown that the coordinate ring of any convex polyomino is inseparable. We introduce the concept of semi-rigidity, and give a combinatorial description of the graphs whose edge ring is semi-rigid. The results are applied to show that for $m-k=k=3$, $G_{k,m-k}$ is not rigid while for $m-k\geq k\geq 4$, $G_{k,m-k}$ is rigid. Here $G_{k,m-k}$ is the complete bipartite graph $K_{m-k,k}$ with one edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and Applications>> 2018, Springer International Publishing AG, part of Springer Natur

Nuclear spin-spin coupling in La_{2-x}Sr_{x}CuO_{4} studied by stimulated echo decay

We have performed copper NQR experiments in high temperature superconductors YBa_{2}Cu_{4}O_{8}, YBa_{2}Cu_{3}O_{7}, and La_{2-x}Sr_{x}CuO_{4} (x=0.12 and 0.15), using the stimulated echo technique. The stimulated echo intensity is analyzed by a model that includes the spin-lattice relaxation process (T_ {1 }-process) and the fluctuating local field due to nuclear spin-spin coupling. The model gives quantitative account of the experimental results in Y-based compounds using the known values of 1/T_{1} and 1/T_{2G}, the gaussian decay rate of the spin echo intensity. The same model applied to LSCO enables us to extract the value of T_{2G}. Our results indicate that T_{1}T/T_{2G} is independent of temperature, implying that the dynamic exponent is one in La_{2-x}Sr_{x}CuO_{4}.Comment: 14 pages, 11 fugures, The bibliography field is correcte

Antiferromagnetic phase transition in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with T_c=55-102 K: Cu- and F-NMR studies

We report on magnetic characteristics in four-layered high-T_c superconductors Ba_2Ca_3Cu_4O_8(F_yO_{1-y})_2 with apical fluorine through Cu- and F-NMR measurements. The substitution of oxygen for fluorine at the apical site increases the carrier density (N_h) and T_c from 55 K up to 102 K. The NMR measurements reveal that antiferromagnetic order, which can uniformly coexist with superconductivity, exists up to N_h = 0.15, which is somewhat smaller than N_h = 0.17 being the quantum critical point (QCP) for five-layered compounds. The fact that the QCP for the four-layered compounds moves to a region of lower carrier density than for five-layered ones ensures that the decrease in the number of CuO_2 layers makes an interlayer magnetic coupling weaker.Comment: 7 pages, 6 gigures, Submitted to J. Phys. Soc. Jp

Experimental Evidence for a Glass forming "Stripe Liquid" in the Magnetic Ground State of La1.65Eu0.2Sr0.15CuO4

We report measurements of the longitudinal ($^{139}T_1^{-1}$) and transverse ($^{139}T_2^{-1}$) decay rates of the magnetization of $^{139}$La nuclei performed in a high quality single crystal of La$_{1.65}$Eu$_{0.2}$Sr$_{0.15}$CuO$_{4}$. We observe a dramatic slowing of the Cu 3d spins manifested as a sharp increase of both $^{139}T_1^{-1}$ and $^{139}T_2^{-1}$ below 30 K. We find that in this temperature range the fluctuations involve a unique time scale $\tau$ which diverges as $(T-T_{\rm A})^{-1.9}$ with $T_{\rm A}\thickapprox 5$ K. This behavior is distinct from the continuous freezing observed in underdoped La$_{1-x}$Sr$_x$CuO$_4$ which involves a distribution of energy barriers. By contrast, in La$_{1.65}$Eu$_{0.2}$Sr$_{0.15}$CuO$_{4}$, the freezing below 30K is intrinsic to its magnetic ground state and the observed power law supports the existence of a glass forming "charge stripe liquid".Comment: 5 pages, 3 Figures. Revised version, resubmitte