This paper reinterprets the economic input-output equation as a description of a realized situation without considering decision making. This paper uses the equation that the self-sufficiency rate is added to the Leontief type, and discusses its solvability. The equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. This condition means that commodities which a part of the relevant society possesses are not all inputted to its inside. Moreover, if the process of input and output is time irreversible, each part of the relevant society satisfies the space-time openness condition. Therefore, the solvability of the equation is guaranteed by time irreversibility. This proposition seems to be relevant to the grandfather paradox which is a type of time paradox.

A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.

Abstract:
The essence of money circulation is that money continues to transfer among economic agents eternally. Based on this recognition, this paper shows a money circulation equation that calculates the quantities of expenditure, revenue, and the end money from the quantity of the beginning money. The beginning money consists of the possession at term beginning, production and being transferred from the outside of the relevant society. The end money consists of the possession at term end, disappearance and transferring to the outside of the relevant society. This equation has a unique solution if and only if each part of the relevant society satisfies the space-time openness condition. Moreover, if money is transferred time irreversibly, each part of the relevant society satisfies the space-time openness condition. Hence, the solvability of the equation is guaranteed by time irreversibility. These solvability conditions are similar to those of the economic input-output equation, but the details are different. An equation resembling our money circulation equation was already shown by Mária Augustinovics, a Hungarian economist. This paper examines the commonalities and differences between our equation and hers. This paper provides the basis for some intended papers by the author.

Abstract:
In a monetary economy, expenditure induces revenue for each agent. We
call this the revenue induction phenomenon. Moreover, in a special case, part
of the expenditure by an agent returns as their own revenue. We call this the
expenditure reflux phenomenon. Although the existence of these phenomena is
known from the olden days, this paper aims to achieve a more precise quantification
of them. We first derive the revenue induction formula through solving the
partial money circulation equation. Then, for a special case, we derive the
expenditure reflux formula. Furthermore, this paper defines the revenue induction
coefficient and the expenditure reflux coefficient, which are the key concepts
for understanding the two formulas, and examines their range.

Abstract:
This paper aims to inquire into an objectively authentic budget constraint in a monetary economy through showing two missing problems of the monetary budget constraint and their solutions. To start with, we show the first missing problem that money is “missing” if all agents expend their total budgets under the simple budget constraint. This problem shows that the simple budget constraint is inadequate as an objective monetary budget constraint. A deficiency of the simple budget constraint exists partly in that it does not reflect money circulation. To improve this deficiency, we incorporate the expenditure reflux formula into the simple constraint. The first missing problem is partially solved by the application of this reflux budget constraint, but another problem occurs. The new problem is that infinite expenditure is permitted under this constraint. This is the second missing problem. The second problem appears to be a variation of the solvability problem of the money circulation equation. Referring to the proof of the solvability, we incorporate a time irreversible disposal into the budget constraint. This irreversibility budget constraint brings us a provisional solution of the missing problems. However, it should not be called a perfect solution. We also examine the relationships between our research and two previous studies: the finance constraint and the cash-in-advance model.

Abstract:
Background: Preoperative chemoradiotherapy (CRT) with 5-FU has been widely used to improve local control of disease and to preserve anal sphincter in the treatment of rectal cancer. UFT and S-1 as oral dihydropyrimidine dehydrogenase (DPD)-inhibitory fluoropyrimidines enhance the therapeutic effect of 5-FU by modulating its metabolic pathways. The purpose of this study was to evaluate the efficacy and toxicity of CRT using UFT versus S-1 in patients with locally advanced rectal cancer. Methods: Fifty-nine patients who received preoperative CRT (40 Gy radiotherapy) were randomly assigned to either UFT or S-1 groups. UFT and S-1 were administered during the radiotherapy course. Response to CRT was determined using a histopathologic examination and RECIST of surgically resected specimens and classified as responders (CR, PR and grade 2, 3) or nonresponders (SD, PD and grade 0, 1). Results: All patients were randomly allocated to S-1 group (n = 30) or UFT group (n = 29). Pathological response rate (Grade2 and Grade3) was 57% in the S-1 group and 45% in the UFT group (p = 0.36). Pathological complete response (CR) rate (Grade3) was 7% in the S-1 group and 4% in the UFT group (p = 0.98). There was no statistically significant difference between the two groups in regard to the response rate of RECIST (p = 0.52). There was no statistically significant difference between the groups based on the downstaging rate, resection of tumor, sphincter preservation and marginal invasion. The incidence of Grade 3 diarrhea was significantly more frequent in the S-1 group (7%) compared with the UFT group (0%) (p = 0.02). Conclusion: The results supported the conclusion that CRT using UFT or S-1 is effective and feasible for patients with locally advanced rectal cancer.

Abstract:
Sustainable sanitation is an approach for more ecological and sustainable water resources management. In this paper, we proposed one of the new integrated waste treatment systems: an “sustainable sanitation system” that includes separation of the black water from water system by a non-flushing toilet (bio-toilet), and a gray water treatment based on a biological and ecological concept. Sustainable sanitation system also converts the domestic waste to soil conditioners and fertilizers, for farmland use. As one of the case studies, Environmentally Symbiotic Housing in which people actually live using the bio-toilet for the black water treatment and the household wastewater treatment facility for the gray water was introduced. The availability of this system was investigated by analyzing the sawdust used in the bio-toilet and the quality of the effluent in the household wastewater treatment facility. As the result, the water content of the sawdust did not exceed 60% in any of the sampling points and the BOD and COD of the effluent of the household wastewater treatment facility were below 10 and 20 mg/L respectively, due to the low loading. Compared to the pollution load on the water environment created by the conventional system, it was found that the effluent of the house has a lower load than the tertiary treatment and the volume of the water consumption is 75% of the conventional system.

Abstract:
Background Maximal oxygen uptake (VO2max) predicts mortality and is associated with endurance performance. Trained subjects have a high VO2max due to a high cardiac output and high metabolic capacity of skeletal muscles. Peroxisome proliferator-activated receptor γ coactivator 1α (PGC-1α), a nuclear receptor coactivator, promotes mitochondrial biogenesis, a fiber-type switch to oxidative fibers, and angiogenesis in skeletal muscle. Because exercise training increases PGC-1α in skeletal muscle, PGC-1α-mediated changes may contribute to the improvement of exercise capacity and VO2max. There are three isoforms of PGC-1α mRNA. PGC-1α-b protein, whose amino terminus is different from PGC-1α-a protein, is a predominant PGC-1α isoform in response to exercise. We investigated whether alterations of skeletal muscle metabolism by overexpression of PGC-1α-b in skeletal muscle, but not heart, would increase VO2max and exercise capacity. Methodology/Principal Findings Transgenic mice showed overexpression of PGC-1α-b protein in skeletal muscle but not in heart. Overexpression of PGC-1α-b promoted mitochondrial biogenesis 4-fold, increased the expression of fatty acid transporters, enhanced angiogenesis in skeletal muscle 1.4 to 2.7-fold, and promoted exercise capacity (expressed by maximum speed) by 35% and peak oxygen uptake by 20%. Across a broad range of either the absolute exercise intensity, or the same relative exercise intensities, lipid oxidation was always higher in the transgenic mice than wild-type littermates, suggesting that lipid is the predominant fuel source for exercise in the transgenic mice. However, muscle glycogen usage during exercise was absent in the transgenic mice. Conclusions/Significance Increased mitochondrial biogenesis, capillaries, and fatty acid transporters in skeletal muscles may contribute to improved exercise capacity via an increase in fatty acid utilization. Increases in PGC-1α-b protein or function might be a useful strategy for sedentary subjects to perform exercise efficiently, which would lead to prevention of life-style related diseases and increased lifespan.

Abstract:
We report the results of millimeter-wave molecular line observations of the Tornado Nebula (G357.7--0.1), which is a bright radio source behind the Galactic Center region. A 15'x15' area was mapped in the J=1--0 lines of CO, 13CO, and HCO+ with the Nobeyama Radio Observatory 45-m telescope. The VLA archival data of OH at 1720 MHz were also reanalyzed. We found two molecular clouds with separate velocities, V_LSR=-14 km/s and +5 km/s. These clouds show rough spatial anti-correlation. Both clouds are associated with OH 1720 MHz emissions in the area overlapping with the Tornado Nebula. The spatial and velocity coincidence indicates violent interaction between the clouds and the Tornado nebula. Modestly excited gas prefers the position of the Tornado "head" in the -14 km/s cloud, also suggesting the interaction. Virial analysis shows that the +5 km/s cloud is more tightly bound by self-gravity than the -14 km/s cloud. We propose a formation scenario for the Tornado Nebula; the +5 km/s cloud collided into the -14 km/s cloud, generating a high-density layer behind the shock front, which activates a putative compact object by Bondi-Hoyle-Lyttleton accretion to eject a pair of bipolar jets.

Abstract:
We have performed unbiased spectral line surveys at 3 mm band toward the Galactic circumnuclear disk (CND) and Sgr A* using the Nobeyama Radio Observatory (NRO) 45 m radio telescope. The target positions are two tangential points of the CND and the direction of Sgr A*. We have obtained three wide-band spectra which cover the frequency range from 81.3 GHz to 115.8 GHz, detecting 46 molecular lines from 30 species including 10 rare isotopomers and four hydrogen recombination lines. Each line profile consists of multiple velocity components which arise from the CND, +50 km/s and +20 km/s clouds (GMCs), and the foreground spiral arms. We define the specific velocity ranges which represent the CND and the GMCs toward each direction, and classify the detected lines into three categories: the CND-/GMC-/HBD-types, based on the line intensities integrated over the defined velocity ranges. The CND- and GMC-types are the lines which mainly trace the CND and the GMCs, respectively. The HBD-type possesses the both characteristics of the CND-/GMC-types. We also present the lists of line intensities and other parameters, as well as intensity ratios, which must be useful to investigate the difference between nuclear environments of our Galaxy and of others.