On the mathematics of the circular flow of economic activity with applications to the topic of caring for the vulnerable during pandemics

We investigate, at the fundamental level, the questions of `why', `when' and `how' one could or should reach out to poor and vulnerable people to support them in the absence of governmental institutions. We provide a simple and new approach that is rooted in linear algebra and basic graph theory to capture the dynamics of income circulation among economic agents. A new linear algebraic model for income circulation is introduced, based on which we are able to categorize societies as fragmented or cohesive. We show that, in the case of fragmented societies, convincing wealthy agents at the top of the social hierarchy to support the poor and vulnerable will be very difficult. We also highlight how linear-algebraic and simple graph-theoretic methods help explain, from a fundamental point of view, some of the mechanics of class struggle in fragmented societies. Then, we explain intuitively and prove mathematically why, in cohesive societies, wealthy agents at the top of the social hierarchy tend to benefit by supporting the vulnerable in their society. A number of new concepts emerge naturally from our mathematical analysis to describe the level of cohesiveness of the society, the number of degrees of separation in business (as opposed to social) networks, and the level of generosity of the overall economy, which all tend to affect the rate at which the top wealthy class recovers its support money back. In the discussion on future perspectives, the connections between the proposed matrix model and statistical physics concepts are highlighted

Quantitative investigation of the homogenising of small glass melts by stirring

The homogenising process in glass was studied by mixing two different glasses, placed in a known initial distribution. The initial orientation was to have a horizontal interface between the two glasses because usually the inhomogeneities lie in parallel horizontal layers in a crucible containing glass unstirred by convection or a mechanical stirrer. The homogeneity was measured quantitatively using an etching and interferometery technique developed in this work. The degree of homogeneity was defined in terms of the intensity of segregation, which varies from one in a fully segregated system to zero in a fully mixed system. Mixing was studied using three different simple stirrers. The intensity of segregation was plotted against number of revolutions of the stirrer. From these graphs it can be seen that the value of intensity of segregation calculated from the etching data has a quantitative significance for following the process of homogenisinatian. The flow patterns observed in thin sections of the glass melts, were completely different from those observed in room temperature model experiments. This was because the glasses mixed were of different viscosities and densities, while the model had used liquids, of equal viscosity and density. The stirrers studied were not very efficient mixing devices but they were designed to compare results in glasses with the previous, room temperature model experiments rather than to be most efficient. The disc stirrer was a convenient standard for comparison of the performance of other stirrers. The addition of a blade to the disc helped in "breaking up the interface "between the two layers. The complex disc stirrer was only efficient when the lower disc was above the liquid-liquid interface. Although no stirrer was extremely efficient, all produced more homogeneous glass than were obtained from unstirred melts

Role of Dietary Crocin in In Vivo Melanoma Tumor Remission

Background: Melanoma is a deadly form of malignancy. Early diagnosis might pave the way to cure but its aggressive nature leads to rapid dissemination and colonization of distant organs. Dietary herbs may play a significant role in prevention of cancer. In this study, we tested anti-tumor efficacy of the Crocus sativus derived active constituent crocin, it is well established to have anti-cancer properties in different cancer models by our group and other groups. Notably, crocin is reported to exert anti-proliferative effect on melanoma cells (B16F10) in vitro. However, roles of crocin on in vivo melanoma tumor remission have not yet been reported to our knowledge. Materials and Methods: Melanoma tumor model was established by transplanting B16F10 (5 X 105) cells into C57BL/6 mice, which were then observed for tumor development and once the tumor volume reached 6 mm, mice were divided into (Group I: tumor-bearing animals treated with normal saline and Group II: counterparts treated with crocin at 2 mg/kg body weight for 21 days). . Tumor remission and tumor growth related parameters such as tumor silent period (TSP), tumor volume doubling time (VDT), growth delay (GD), and mean survival time (MST) were determined. In addition, serum protein profiles were analyzed. Results: The 21 days crocin treatment significantly reduced the tumor burden in mice, extending the mean survival time significantly as compared to control. Crocin treatment also significantly increased the TGD and TSP and decreased VDT. Furthermore, while serum proteins such as albumin and globulin (alpha1, alpha2, beta, and gamma) were altered due to tumor burden, crocin treatment resulted in their levels near to normal at the end of the experimental period. Conclusion: Our study provided clear evidence that crocin may exhibit significant melanoma tumor remission properties by positively modulating tumor growth related parameters. In future, the molecular mechanisms of crocin action should be studied extensively in melanoma models before defining crocin-based melanoma drug formulation

Modeling and analysis of flutter-based thin-film cantilever microgenerator

This paper presents a model for design and analysis of flutter-based microgenerators and a new concept for wind energy harvesting using thin-film cantilever with coils embedded on the sides of the cantilever. The analytical model predicts the flow-induced response of the thin-film cantilever at various parameters as well as the frequency of flutter at a wind speed which is crucial for designing a flutter based microgenerator. A complete analytical model unites various physics involved, flow induced forces on the cantilever, mechanical vibrations, electromagnetic coupling, and electric power output. The flutter frequency predicted by the analytical model is verified against finite element analysis using NASTRAN. The effect of span, width of the cantilever, length of coil on the cantilever and load resistance is investigated on the performance of the harvester. The results predicted by the analytical model agree reasonably well with the finite element analysis results paving way of using such an analytical model to design and optimize a fluttering wind energy harvester

Pantoprazole infusion as adjuvant therapy to endoscopic treatment in patients with peptic ulcer bleeding: Prospective randomized controlled trial

Abstract Background and Aim: Following successful endoscopic therapy in patients with peptic ulcer bleeding, rebleeding occurs in 20% of patients. Rebleeding remains the most important determinant of poor prognosis. We investigated whether or not administration of pantoprazole infusion would improve the outcome in ulcer bleeding following successful endoscopic therapy. Methods: In this double-blind, placebo-controlled, prospective trial, patients who had gastric or duodenal ulcers with active bleeding or non-bleeding visible vessel received combined endoscopy therapy with injection of epinephrine and heater probe application. Patients who achieved hemostasis were randomly assigned to receive pantoprazole (80 mg intravenous bolus followed by an infusion at a rate of 8 mg per hour) or placebo for 72 h. The primary end-point was the rate of rebleeding. Results: Rebleeding was lower in the pantoprazole group (8 of 102 patients, 7.8%) than in the placebo group (20 of 101 patients, 19.8%; P = 0.01). Patients in the pantoprazole group required significantly fewer transfusions (1 ± 2.5 vs 2 ± 3.3; P = 0.003) and days of hospitalization (5.6 ± 5.3 vs 7.7 ± 7.3; P = 0.0003). Rescue therapies were needed more frequently in the placebo group (7.8% vs 19.8%; P = 0.01). Three (2.9%) patients in the pantoprazole group and eight (7.9%) in the placebo group required surgery to control their bleeding ( P = 0.12). Two patients in the pantoprazole group and four in the placebo group died ( P = 0.45). Conclusion: In patients with bleeding peptic ulcers, the use of high dose pantoprazole infusion following successful endoscopic therapy is effective in reducing rebleeding, transfusion requirements and hospital stay

Prospective, randomized and controlled study of the efficacy of rabeprozole and placebo in the treatment of nonerosive reflux disease.

Background: Nonerosive reflux disease is defined as the presence of typical symptoms of gastroesophageal reflux disease in absence of visible esophageal mucosal injury at endoscopy. 24 hour ph study is needed to define the sub group. Treatment with the acid inhibitory agents is effective, proton pump inhibitors are most effective form of therapy. Clinical results to date suggest that anti-secretory therapy may be less effective in providing symptom relief for the patients nonerosive reflux disease than the patients with erosive disease. Objective: To assess prospectively effectiveness of proton pump inhibitors in nonerosive reflux disease Methods: A total of 200 patients with nonerosive reflux disease were randomized to receive placebo (98) or rabeprozole (102) for 6 months, with consultations at 3 weeks, 6 weeks, and 6 months. The primary end points were change in the severity of heart burn and regurgitation at the above mention periods. Results: Demographics of the randomized in each group were comparable except that placebo group included more males. The baseline characteristics between two groups were similar. After 6 month of treatment, reduction of visual analogue scale (VAS) of heartburn was prominent in treatment group (63% vs. 15%). At 3 weeks and six weeks, treatment group showed greater reduction of VAS for heart burn (p<0.01). Patients of the treatment group had lower frequency of heartburn (p<0.01) and regurgitation (p<0.01) at the end of the 6 month treatment. For the adverse effects, there was no difference in the both groups. Conclusions: Rabeprozole was more effective than placebo of the treatment of symptoms presented by the patients with nonerosive reflux disease, who had positive 24 hour ph study