Metaphysics of a forgotten tradition I. Introduction of the concept of “intrinsic modus of thing” by John Duns Scotus: From the theological explication of “infinity” to the metaphysical problem of “contraction of being”

The article is the first part of a study on the notion of the “intrinsic modus” of thing or reality in the metaphysics of the early Scotist tradition (first quarter of the 14th century). This part of the study analyses the circumstances of the first formulation of the notion of “modus intrinsecus” in the theological writings of John Duns Scotus and identifies two main (and one additional) contexts for Scotus’s explication of this concept, which will be important for the subsequent Scotistic tradition of meta[1]physics. The article then puts forward a hypothesis about a historical shift in the use of this concept based on an analysis of Scotus’s texts. Scotus initially introduces it solely for a theological explanation of the concept of “infinite being”, but later, in connection with his discussion of the reality of the concept of being, uses the concept of intrinsic mode as key to his own solution to the metaphysical problem of the “contraction” of the transcendental concept of being, which he thinks of as a particular “modification”. Finally, the article identifies the main structural elements in Scotus’s discussion of “intrinsic mode” and attempts to present the content of this concept by distinguishing between intrinsic mode and Scotus’s other related metaphysical concepts (quiddity, difference, property).

Limit Points and Separation Axioms with Respect to Supra Semi-open Sets

Sometimes we need to minimize the conditions of topology for different reasons such as obtaining more convenient structures to describe some real-life problems, or constructing some counterexamples whom show the interrelations between certain topological concepts, or preserving some properties under fewer conditions of those on topology. To contribute this research area, in this paper, we establish some new concepts on supra topological spaces using supra semi-open sets and give some characterizations of them. First, we introduce a concept of supra semi limit points of a set and study main properties, in particular, on the spaces that possess the difference property. Second, we define and investigate new separation axioms, namely supra semi Ti-spaces (i = 0, 1, 2, 3, 4) and give complete descriptions for each one of them. We provide some examples to show the relationships between them as well as with STi-space.

Some Applications of Supra Preopen Sets

The aim of this work is to define some concepts on supra topological spaces using supra preopen sets and investigate main properties. We started this paper by correcting some results obtained in previous study and presenting further properties of supra preopen sets. Then, we introduce a concept of supra prehomeomorphism maps and discuss its main properties. After that we explore the concepts of supra limit and supra boundary points of a set with respect to supra preopen sets and examine their behaviours on the spaces that possess the difference property. Finally, we formulate the concepts of supra pre-Ti-spaces i=0,1,2,3,4 and give completely descriptions for each one of them. In general, we study their main properties in detail and show the implications of these separation axioms among themselves as well as with STi-space with the help of some interesting examples.

Optimal Common Contract with Heterogeneous Agents

We consider the principal-agent problem with heterogeneous agents. Previous works assume that the principal signs independent incentive contracts with every agent to make them invest more efforts on the tasks. However, in many circumstances, these contracts need to be identical for the sake of fairness. We investigate the optimal common contract problem. To our knowledge, this is the first attempt to consider this natural and important generalization. We first show this problem is NP-complete. Then we provide a dynamic programming algorithm to compute the optimal contract in O(n2m) time, where n,m are the number of agents and actions, under the assumption that the agents' cost functions obey increasing difference property. At last, we generalize the setting such that each agent can choose to directly produce a reward in [0,1]. We provide an O(log n)-approximate algorithm for this generalization.

The First Difference Property of the Present Value Operator

This paper identifies a fundamental relationship between the present value of a given cash flow and the present value of the period by period change in that cash flow. The new relationship is shown to be highly useful for the identification of analytic expressions for present value and related measures such as duration and convexity; expressions that continue to play an instructive role by helping to relate the quantitative outcomes of numerical calculations to the driving forces behind those calculations. This new method applies only simple arithmetic operations and avoids the use of differential calculus and advanced series summation in order to derive these analytic results. We apply the method to a variety of nontraditional cash flows, including cash flows with linear growth or decay, cash flows that are subject to different tax effects for dividends and capital gain, and cash flows that are projected to exhibit cyclical variation over time.