On the Accuracy of Finite Difference Solution for Dirichlet Problems

Let $\Omega$ be a bounded domain of $\mathrm{R}^{2}$ and consider the Dirichlet problem $-\triangle u+c(x, y)u$ $=f(x, y)$ in $\Omega$ (1.1) $u$ $=g(x, y)$ on $\Gamma=\partial\Omega$ (1.2) where $c,f$ and $g$ are given functions satisfying $c\geq 0$, $c,$ $f\in C^{0,\alpha}(\Omega)=C\alpha(\Omega)$ and $g\in C(\Gamma)$ with the H\"older exponent $\alpha\in(0,1)$. Then it is known $[2,4]$ that there exists a unique solution $u\in C(\overline{\Omega})\cap C^{2,\alpha}(\Omega)$ of (1.1) and (1.2). Furthermore, if $l$ is a nonnegative integer, $c,$ $f\in C^{l,\alpha}(\overline{\Omega})$ , $g\in c^{l2,\alpha}+(\overline{\Omega})$ and $\Omega$ is a $C^{l+2,\alpha}$ domain, then it is also known that $u\in C^{l+2,\alpha}(\overline{\Omega})$. (1.3) Finite difference methods for solving the problem $(1.1)-(1.2)$ have extensively been studied in much literature (e.g., $[3],[5- 6],[8- 9],[12]$ ) usually for the case $u\in C^{4}(\overline{\Omega})$. We can find there many estimates on the accuracy of finite difference formulas. The accuracy of the formula, however, does not necessarily imply that of the approximat

Gravitational waves from black hole-neutron star binaries I: Classification of waveforms

Using our new numerical-relativity code SACRA, long-term simulations for inspiral and merger of black hole (BH)-neutron star (NS) binaries are performed, focusing particularly on gravitational waveforms. As the initial conditions, BH-NS binaries in a quasiequilibrium state are prepared in a modified version of the moving-puncture approach. The BH is modeled by a nonspinning moving puncture and for the NS, a polytropic equation of state with $\Gamma=2$ and the irrotational velocity field are employed. The mass ratio of the BH to the NS, $Q=M_{\rm BH}/M_{\rm NS}$, is chosen in the range between 1.5 and 5. The compactness of the NS, defined by ${\cal C}=GM_{\rm NS}/c^2R_{\rm NS}$, is chosen to be between 0.145 and 0.178. For a large value of $Q$ for which the NS is not tidally disrupted and is simply swallowed by the BH, gravitational waves are characterized by inspiral, merger, and ringdown waveforms. In this case, the waveforms are qualitatively the same as that from BH-BH binaries. For a sufficiently small value of Q \alt 2, the NS may be tidally disrupted before it is swallowed by the BH. In this case, the amplitude of the merger and ringdown waveforms is very low, and thus, gravitational waves are characterized by the inspiral waveform and subsequent quick damping. The difference in the merger and ringdown waveforms is clearly reflected in the spectrum shape and in the "cut-off" frequency above which the spectrum amplitude steeply decreases. When an NS is not tidally disrupted (e.g., for Q=5), kick velocity, induced by asymmetric gravitational wave emission, agrees approximately with that derived for the merger of BH-BH binaries, whereas for the case that the tidal disruption occurs, the kick velocity is significantly suppressed.Comment: 25 pages, 3 jpg figures, accepted for publication in PRD; erratum is added on Jul 23. 201

Immunohistochemical Analysis of Colorectal Cancer among Atomic Bomb Survivors in Hiroshima

In order to elucidate the biological characteristics of colorectal cancer among atomic bomb survivors in Hiroshima, a total of 159 cases of colorectal cancers comprising 73 cases in exposed atomic bomb survivors and 86 cases in non-exposed individuals were examined histologically and immunohistochemically for various functioning proteins. No statistical differences could be demonstrated in the incidence of various marker expressions of colorectal cancers between the exposed group and control group. However, comparison by the site of colorectal cancer showed that sigmoid colon cancers in the exposed group or high dose group showed a significantly higher frequency of glycoproteins such as α1-antichymotrypsin (ACT), secretory component (SC), α1-antitrypsin (AAT), and human chorionic gonadotropin (HCG) when compared with the control group. These results correlated well with the epidemiological data that the radiation effect on the incidence of colorectal cancer in atomic bomb survivors was most remarkable in the sigmoid colon.This study was supported in part by Grants in Aid for Cancer Research from the Ministry of Education, Science and Culture, Japan

Simulating coalescing compact binaries by a new code SACRA

We report our new code (named SACRA) for numerical relativity simulations in which an adaptive mesh refinement algorithm is implemented. In this code, the Einstein equations are solved in the BSSN formalism with a fourth-order finite differencing, and the hydrodynamic equations are solved by a third-order high-resolution central scheme. The fourth-order Runge-Kutta scheme is adopted for integration in time. To test the code, simulations for coalescence of black hole-black hole (BH-BH), neutron star-neutron star (NS-NS), and black hole-neutron star (BH-NS) binaries are performed, and also, properties of BHs formed after the merger and gravitational waveforms are compared among those three cases. For the simulations of BH-BH binaries, we adopt the same initial conditions as those by Buonanno et al. and compare numerical results. We find reasonable agreement except for a slight disagreement possibly associated with the difference in choice of gauge conditions and numerical schemes. For an NS-NS binary, we performed simulations employing both SACRA and Shibata's previous code, and find reasonable agreement. For a BH-NS binary, we compare numerical results with our previous ones, and find that gravitational waveforms and properties of the BH formed after the merger agree well with those of our previous ones, although the disk mass formed after the merger is less than 0.1% of the total rest mass, which disagrees with the previous result. We also report numerical results of a longterm simulation (with $\sim 4$ orbits) for a BH-NS binary for the first time. All these numerical results show behavior of convergence, and extrapolated numerical results for time spent in the inspiral phase agree with post-Newtonian predictions in a reasonable accuracy.Comment: PRD in press. Typos are corrected, and references are adde

Construction and reliability of the Japanese version of the Adolescent Egocentrism-Sociocentrism (AES) scale and its preliminary application in the Japanese university students

In recent years, the problem of interpersonal relationships has been reported to be associated with various adolescent psychiatric problems. Egocentrism is one factor related to the problem of interpersonal relationships. The Adolescent Egocentrism- Sociocentrism (AES) scale is used to assess egocentrism in Western countries, but no such scale has been developed in Japan. The purpose of our current study was to develop the Japanese version of the AES scale and investigate the relationship between the egocentrism assessed by the AES scale and the self -consciousness assessed by the Japanese version of the self -consciousness scale. The original version of the AES scale was first translated into Japanese using the forwardbackward method and examined for factorial reliability and validity. The results demonstrated that the Japanese version of the AES scale shows adequate factorial reliability and validity, but different from the original version the “egocentrism personal fable” subscale which measures the feeling that oneself is special and unique was not extracted in the Japanese version. We found a moderate correlation between the non- social focuses of the AES scale and the public self -consciousness subscale of the self –consciousness scale. This correlation suggests that a strong attention of others’ view on oneself results in the avoidance of others. The Japanese version of the AES scale can examine egocentrism adequately together with sociocentrism and non- social focuses. As this scale is self -reporting and easy to complete, it may have practical utility in a clinical setting

Label-free Evaluation of Myocardial Infarct in Surgically Excised Ventricular Myocardium by Raman Spectroscopy

Understanding the viability of the ischemic myocardial tissue is a critical issue in determining the appropriate surgical procedure for patients with chronic heart failure after myocardial infarction (MI). Conventional MI evaluation methods are; however, preoperatively performed and/or give an indirect information of myocardial viability such as shape, color, and blood flow. In this study, we realize the evaluation of MI in patients undergoing cardiac surgery by Raman spectroscopy under label-free conditions, which is based on intrinsic molecular constituents related to myocardial viability. We identify key signatures of Raman spectra for the evaluation of myocardial viability by evaluating the infarct border zone myocardium that were excised from five patients under surgical ventricular restoration. We also obtain a prediction model to differentiate the infarcted myocardium from the non-infarcted myocardium by applying partial least squares regression-discriminant analysis (PLS-DA) to the Raman spectra. Our prediction model enables identification of the infarcted tissues and the non-infarcted tissues with sensitivities of 99.98% and 99.92%, respectively. Furthermore, the prediction model of the Raman images of the infarct border zone enabled us to visualize boundaries between these distinct regions. Our novel application of Raman spectroscopy to the human heart would be a useful means for the detection of myocardial viability during surgery