Dynamic Ecological System Analysis

This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning methodologies through which compartmental systems are decomposed to the utmost level. The dynamic system and subsystem partitioning enable tracking the evolution of the initial stocks, environmental inputs, and intercompartmental system flows, as well as the associated storages derived from these stocks, inputs, and flows individually and separately within the system. Moreover, the transient and the dynamic direct, indirect, acyclic, cycling, and transfer (diact) flows and associated storages transmitted along a given flow path or from one compartment, directly or indirectly, to any other are analytically characterized, systematically classified, and mathematically formulated. Further, the article develops a dynamic technique based on the diact transactions for the quantitative classification of interspecific interactions and the determination of their strength within food webs. Major concepts and quantities of the current static network analyses are also extended to nonlinear dynamic settings and integrated with the proposed dynamic measures and indices within the proposed unifying mathematical framework. Therefore, the proposed methodology enables a holistic view and analysis of ecological systems. We consider that this methodology brings a novel complex system theory to the service of urgent and challenging environmental problems of the day and has the potential to lead the way to a more formalistic ecological science.Comment: 45 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1811.11885, arXiv:1811.1042

A Medical Waste Sterilizer

Sterilization of medical waste is very important for the environment, as the exposition may result in various diseases because of viral or bacterial content of the waste. There are devices developed for this purpose aiming to sterilize the waste in a form called batch process, meaning that a certain amount of waste is placed into the system and subjected to a sterilization procedure for a while and removed from the system afterwards. The procedure is repeated by the next set of waste till the whole set is sterilized. Our aim, however, is to design a device, a rotating cylindrical container having tubular lights attached to the walls inside, through which the waste is exposed to ultraviolet light as it gets rotated and moved towards the exit. The process will continue till the whole set is fed into the system. Such a device would be more effective as compared to batch processing types. The study group is asked to develop a mathematical model to analyse the effect of the number and location of tubes which will lead to maximal exposure during certain amount of time, which also needs an estimate, the sample will reside in the device before it gets discharged

Effective bounds on ampleness of cotangent bundles

We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1, \dots, d_c$ in $\mathbb{P}^N$ has ample cotangent bundle if $c \geq 2n-2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic in $n$. This degree bound substantially improves the currently best-known super-exponential bound in $N$ by Deng, although our result does not address the case $n \leq c < 2n-2$.Comment: Uses a result of Darondeau to improve the bound

Financial Engineering and Engineering of Financial Regulation

As observed at least in last two decades, financial engineering has not only changed the way of doing business in finance world, but also has changed daily life of average citizens in the leading economies. Structured products named as weapons of mass destruction in some post-crisis comments. But it is fair to say that few people could understand the nature and risks of these instruments before the crisis. By using literature review and case study analysis, the author analyses how financial regulation and supervision have failed to understand/manage the financial engineering products during/before the global financial crisis. In this context, we discuss the measures to enhance good regulatory governance in engineered products. We conclude however engineered products have important benefits to the global economy, regulatory/supervisory structure should be improved for better firm/system wide risk management. Secondly, there are four components to improve prudential regulatory/supervisory framework of structured products. Those are, timely/effectively action to the balance sheet problems, to increase the effectiveness of the risk management, to improve independence and quality of prudential regulation/supervision and to increase accountability of supervisors.Financial engineering, structured finance, financial crisis, risk management, regulation