Polyominoes and Polyiamonds as Fundamental Domains of Isohedral Tilings with Rotational Symmetry

We describe computer algorithms that produce the complete set of isohedral tilings by n-omino or n-iamond tiles in which the tiles are fundamental domains and the tilings have 3-, 4-, or 6-fold rotational symmetry. The symmetry groups of such tilings are of types p3, p31m, p4, p4g, and p6. There are no isohedral tilings with symmetry groups p3m1, p4m, or p6m that have polyominoes or polyiamonds as fundamental domains. We display the algorithms' output and give enumeration tables for small values of n. This expands on our earlier works (Fukuda et al 2006, 2008)

Exact Solutions v.s. Perturbative Calculations of Finite Φ3\Phi^{3}-Φ4\Phi^{4} Hybrid-Matrix-Model

There is a matrix model corresponding to a scalar field theory called Grosse-Wulkenhaar model, which is renormalizable by adding a harmonic oscillator potential to scalar $\Phi^{4}$ theory on Moyal spaces. There are more unknowns in $\Phi^{4}$ matrix model than in $\Phi^{3}$ matrix model, for example, in terms of integrability. We then construct a one-matrix model ($\Phi^{3}$-$\Phi^{4}$ Hybrid-Matrix-Model) with multiple potentials, which is a combination of a $3$-point interaction and a $4$-point interaction, where the $3$-point interaction of $\Phi^{3}$ is multiplied by some positive definite diagonal matrix $M$. This model is solvable due to the effect of this $M$. In particular, the connected $\displaystyle\sum_{i=1}^{B}N_{i}$-point function $G_{|a_{N_{1}}^{1}\cdots a_{N_{1}}^{1}|\cdots|a_{1}^{B}\cdots a_{N_{B}}^{B}|}$ of $\Phi^{3}$-$\Phi^{4}$ Hybrid-Matrix-Model is studied in detail. This $\displaystyle\sum_{i=1}^{B}N_{i}$-point function can be interpreted geometrically and corresponds to the sum over all Feynman diagrams (ribbon graphs) drawn on Riemann surfaces with $B$ boundaries (punctures). Each $|a_{1}^{i}\cdots a_{N_{i}}^{i}|$ represents $N_{i}$ external lines coming from the $i$-th boundary (puncture) in each Feynman diagram. First, we construct Feynman rules for $\Phi^{3}$-$\Phi^{4}$ Hybrid-Matrix-Model and calculate perturbative expansions of some multipoint functions in ordinary methods. Second, we calculate the path integral of the partition function $\mathcal{Z}[J]$ and use the result to compute exact solutions for $1$-point function $G_{|a|}$ with $1$-boundary, $2$-point function $G_{|ab|}$ with $1$-boundary, $2$-point function $G_{|a|b|}$ with $2$-boundaries, and $n$-point function $G_{|a^{1}|a^{2}|\cdots|a^{n}|}$ with $n$-boundaries. They include contributions from Feynman diagrams corresponding to nonplanar Feynman diagrams or higher genus surfaces.Comment: 28 pages. Typos were corrected, three references were added, and an annotation was added in Section

Exact solution of the Φ23\Phi_{2}^{3} finite matrix model

We find the exact solutions of the $\Phi_{2}^{3}$ finite matrix model (Grosse-Wulkenhaar model). In the $\Phi_{2}^{3}$ finite matrix model, multipoint correlation functions are expressed as $G_{|a_{1}^{1}\ldots a_{N_{1}}^{1}|\ldots|a_{1}^{B}\ldots a_{N_{B}}^{B}|}$. The $\displaystyle \sum_{i=1}^{B}N_{i}$-point function denoted by $G_{|a_{1}^{1}\ldots a_{N_{1}}^{1}|\ldots|a_{1}^{B}\ldots a_{N_{B}}^{B}|}$ is given by the sum over all Feynman diagrams (ribbon graphs) on Riemann surfaces with $B$-boundaries, and each $|a^{i}_{1}\cdots a^{i}_{N_{i}}|$ corresponds to the Feynman diagrams having $N_{i}$-external lines from the $i$-th boundary. It is known that any $G_{|a_{1}^{1}\ldots a_{N_{1}}^{1}|\ldots|a_{1}^{B}\ldots a_{N_{B}}^{B}|}$ can be expressed using $G_{|a^{1}|\ldots|a^{n}|}$ type $n$-point functions. Thus we focus on rigorous calculations of $G_{|a^{1}|\ldots|a^{n}|}$. The formula for $G_{|a^{1}|\ldots|a^{n}|}$ is obtained, and it is achieved by using the partition function $\mathcal{Z}[J]$ calculated by the Harish-Chandra-Itzykson-Zuber integral. We give $G_{|a|}$, $G_{|ab|}$, $G_{|a|b|}$, and $G_{|a|b|c|}$ as the specific simple examples. All of them are described by using the Airy functions.Comment: 19 pages, no figure, Some mistakes are revised in i

High Field Magnetization in Manganese Intermetallic Compounds(Magnetism)

Magnetization measurements were carried out on manganese intermetallic compounds Mn_3MC(M=Ga, Zn), Mn_Co_xSb(x=0.09 and 0.15) and MnMX(M=Ru, Rh, Pd;X=As, P)in magnetic fields up to 150 or 320 kOe. Antiferromagnetic(AF)-ferromagnetic(F) field-induced transitions and (AF+F)-(F) one were observed for Mn_3GaC and Mn_3ZnC, respectively. For Mn_Co_Sb, intermediate(I)- ferrimagnetic(Fr) field-induced transitions were observed. For Mn_Co_Sb, AF-Fr field-induced transitions were observed. These transitions were of the first order except one of Mn_3ZnC. The magnetic properties of MnMX (M=Ru, Rh, Pd;X=As, P) were discussed on the basis of the values of magnetization and high-field magnetic susceptibility

Real symmetric Φ4\Phi^4-matrix model as Calogero-Moser model

We study a real symmetric $\Phi^4$-matrix model whose kinetic term is given by $\mathrm{Tr}( E \Phi^2)$, where $E$ is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Sch\"odinger type equation with Calogero-Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.Comment: 13 pages, no figur

Novel Magnetic and Thermodynamic Properties of Thiospinel Compound CuCrZrS4_{4}

We have carried out dc magnetic susceptibility, magnetization and specific heat measurements on thiospinel CuCrZrS$_{4}$. Below $T_{\rm C}^{*} =$ 58 K, dc magnetic susceptibility and magnetization data show ferromagnetic behavior with a small spontaneous magnetization 0.27 $\mu_{\rm B}/$f. u.. In dc magnetic susceptibility, large and weak irreversibilities are observed below $T_{\rm f} =$ 6 K and in the range $T_{\rm f}< T < T_{\rm C}^{*}$ respectively. We found that there is no anomaly as a peak or step in the specific heat at $T_{\rm C}^{*}$.Comment: 11 pages, 4 figure

Videogame e cultura : análise dos aspectos culturais na localização de videogame

Na indústria dos videogames, localização é o processo de adaptação pelo qual um jogo passa para que seja vendido em diferentes idiomas e países. Também conhecidos como softwares de entretenimento ou games, os videogames são atualmente desenvolvidos com a globalização em mente, permitindo uma flexibilidade maior para adequá-los a diferentes mercados, culturas e idiomas, facilitando o processo de localização por parte do tradutor — o que, por muitas vezes, prova-se um grande desafio. Este trabalho visa analisar como fatores culturais influenciam o processo de localização de videogames, utilizando como material de estudo obras originais e localizadas de videogames nas línguas portuguesa, inglesa e japonesa, com o objetivo final de alimentar uma reflexão mais aprofundada acerca da importância que a cultura tem nesse processo para o tradutor e para os desenvolvedores na indústria.In the video game industry, localization is the adaptation process that a game goes through to be sold in different languages and countries. Also known as games or entertainment software, video games are currently developed with globalization in mind, allowing greater flexibility to adapt them to different markets, cultures and languages, facilitating the localization process by the translator – which, more often than not, proves to be a great challenge. This work aims to analyze how cultural factors influence the video game localization process, by using original and localized video game works in Portuguese, English and Japanese as study material, with the end goal of fostering a deeper thought on the importance that culture has in this process for the translator and for the developers in the industry

Large negative magnetoresistance in thiospinel CuCrZrS4

We report on large negative magnetoresistance observed in ferromagnetic thiospinel compound CuCrZrS$_{4}$. Electrical resistivity increased with decreasing temperature according to the form proportional to $\textrm{exp}(T_{0}/T)^{1/2}$, derived from variable range hopping with strong electron-electron interaction. Resistivity under magnetic fields was expressed by the same form with the characteristic temperature T0 decreasing with increasing magnetic field. Magnetoresistance ratio $\rho (T,0)/\rho(T,H)$ is 1.5 at 100 K for H=90 kOe and increases divergently with decreasing temperature reaching 80 at 16 K. Results of magnetization measurements are also presented. Possible mechanism of the large magnetoresistance is discussed.Comment: 9 pages, 5 figures, to be published in Solid State Commu