General theory for integer-type algorithm for higher order differential equations

Based on functional analysis, we propose an algorithm for finite-norm solutions of higher-order linear Fuchsian-type ordinary differential equations (ODEs) P(x,d/dx)f(x)=0 with P(x,d/dx):=[\sum_m p_m (x) (d/dx)^m] by using only the four arithmetical operations on integers. This algorithm is based on a band-diagonal matrix representation of the differential operator P(x,d/dx), though it is quite different from the usual Galerkin methods. This representation is made for the respective CONSs of the input Hilbert space H and the output Hilbert space H' of P(x,d/dx). This band-diagonal matrix enables the construction of a recursive algorithm for solving the ODE. However, a solution of the simultaneous linear equations represented by this matrix does not necessarily correspond to the true solution of ODE. We show that when this solution is an l^2 sequence, it corresponds to the true solution of ODE. We invent a method based on an integer-type algorithm for extracting only l^2 components. Further, the concrete choice of Hilbert spaces H and H' is also given for our algorithm when p_m is a polynomial or a rational function with rational coefficients. We check how our algorithm works based on several numerical demonstrations related to special functions, where the results show that the accuracy of our method is extremely high.Comment: Errors concerning numbering of figures are fixe

Establishing baseline criteria of cardio-ankle vascular index as a new indicator of arteriosclerosis: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>A cardio-ankle vascular index (CAVI) has been developed to represent the extent of arteriosclerosis throughout the aorta, femoral artery and tibial artery independent of blood pressure. To practically use CAVI as a diagnostic tool for determining the extent of arteriosclerosis, our study objectives were (1) to establish the baseline CAVI scores by age and gender among cardiovascular disease (CVD) risk-free persons, (2) to compare CAVI scores between genders to test the hypothesis that the extent of arteriosclerosis in men is greater than in women, and (3) to compare CAVI scores between the CVD risk-free group and the CVD high-risk group in order to test the hypothesis that the extent of arteriosclerosis in the CVD high-risk group is greater than in the CVD risk-free group.</p> <p>Methods</p> <p>Study subjects were 32,627 urban residents 20-74 years of age who participated in CVD screening in Japan during 2004-2006. A new device (model VaSera VS-1000) was used to measure CAVI scores. At the time of screening, CVD high-risk persons were defined as those having any clinical abnormalities of CVD, and CVD risk-free persons were defined as those without any clinical abnormalities of CVD. Age-specific average CAVI scores were compared between genders and between the CVD risk-free group and the CVD high-risk group. Student's t-test using two independent samples was applied to a comparison of means between two groups.</p> <p>Results</p> <p>Average age-specific baseline scores of CAVI in the CVD risk-free group linearly increased in both genders as their age increased. Average age-specific baseline scores of CAVI in the CVD risk-free group were significantly greater among men than among women. Average age-specific baseline scores of CAVI in the CVD risk-free group were significantly smaller than those in the CVD high-risk group in both genders after 40 years of age.</p> <p>Conclusions</p> <p>The baseline CAVI scores from the CVD risk-free group are useful for future studies as control values. The CAVI method is a useful tool to screen persons with moderate to advanced levels of arteriosclerosis.</p

Intraductal Tubular Carcinoma of the Pancreas: a Case Report with the Imaging Findings

We describe here a case of intraductal tubular carcinoma of the main pancreatic duct. Gadolinium-enhanced pancreas magnetic resonance (MR) imaging showed an enhancing mass that was confined in the dilated main pancreatic duct of the pancreatic body, along with dilatation of the upstream main pancreatic duct and chronic pancreatitis that was due to obstruction. MR cholangiopancreatography and an endoscopic retrograde pancreatogram showed a filling defect that was due to an intraductal mass of the pancreatic body, along with dilatation of the upstream main pancreatic duct and no dilatation of the downstream main pancreatic duct. The pathological findings demonstrated an intraductal nodular appearance without papillary projection or mucin hypersecretion

Impact of postoperative complications after primary tumor resection on survival in patients with incurable stage IV colorectal cancer: A multicenter retrospective cohort study

[Aims] Primary tumor resection for patients with incurable stage IV colorectal cancer can prevent tumor-related complications but may cause postoperative complications. Postoperative complications delay the administration of chemotherapy and can lead to the spread of malignancy. However, the impact of postoperative complications after primary tumor resection on survival in patients with incurable stage IV colorectal cancer remains unclear. Therefore, this study aimed to investigate how postoperative complications after primary tumor resection affect survival in this patient group. [Methods] We reviewed data on 966 patients with stage IV colorectal cancer who underwent palliative primary tumor resection between January 2006 and December 2007. We examined the association between major complications (National Cancer Institute Common Terminology Criteria for Adverse Events v3.0 grade 3 or more) and overall survival using Cox proportional hazard model and explored risk factors associated with major complications using multivariable logistic regression analysis. [Results] Ninety-three patients (9.6%) had major complications. The 2-year overall survival rate was 32.7% in the group with major complications and 50.3% in the group with no major complications. Patients with major complications had a significantly poorer prognosis than those without major complications (hazard ratio: 1.62; 95% confidence interval: 1.21-2.18; P < .01). Male, rectal tumor, and open surgery were identified to be risk factors for major complications. [Conclusions] Postoperative complications after primary tumor resection was associated with decreased long-term survival in patients with incurable stage IV colorectal cancer

Welfare and Equity Impacts of Cross-Border Factor Mobility in Bangladesh: A General Equilibrium Analysis

Bangladesh is one of the top remittance recipient countries in the world and it is the second largest source of the country’s foreign exchange earnings. However, in recent years, remittance inflows into Bangladesh have declined steadily because of real income reductions of migrants. This trend in income has increased the number of returning migrants, making domestic employment less secure. To address this issue, we develop a recursive dynamic CGE model for Bangladesh that describes the allocation of employment between domestic and foreign labor markets in response to a foreign wage premium, competition between local firms and multinational enterprises in the ready-made garments (RMG) sector, and distributional impacts of factor mobility on different household groups. Our simulation results show that returning migrants reduce household welfare by lowering wages and increasing unemployment, particularly for unskilled workers in the domestic labor market. Using counteractive policy options, we examine the impacts of FDI promotion in the RMG sector and of a human-capital development program. Based on our results, we conclude that the former policy minimizes the negative impacts of foreign labor market shocks, while a combination of both policies is more equitable.JEL Classification Codes: C68, F21, F22, O15It is gratefully acknowledged that this study was supported by the JSPS KAKENHI Grants (18J11669 and 16K03613).http://www.grips.ac.jp/list/jp/facultyinfo/hosoe_nobuhiro