Living on the edge: how risky is it to operate at the limit of the tolerated risk?

This paper studies some of the implicit risks associated with strategies followed by a risk averse investor who maximizes the expected value of his final wealth, subject to a risk tolerance constraint characterized in terms of a convex risk measure such as Conditional Value-at-Risk. Embedded probability measures are uncovered using duality theory; these are used to assess the probability of surpassing a standard Value-at-Risk threshold. Using one of these embedded probabilities, a closed-form measure of the financial cost of hedging the loss exposure associated to the optimal strategies is derived and shown to be, under certain assumptions, a coherent measure of risk.     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

On the necessity of the assumptions used to prove Hardy–Littlewood and Riesz rearrangement inequalities

We prove that supermodularity is a necessary condition for the generalized Hardy–Littlewood and Riesz rearrangement inequalities. We also show the necessity of the monotonicity of the kernels involved in the Riesz-type integral.     

Chance and probability: What do they mean to university engineering students?

The great interest aroused by the incorporation of Statistics and Probability into curricular projects has been accompanied by considerable evidence of significant difficulties in the meaningful learning and application of the concepts. These difficulties have been the subject of many studies, mostly concerning secondary school students. This study seeks to investigate the level of understanding of random phenomena, in a group of university students, on the second year of a Technical and Industrial Engineering Degree at the University of the Basque Country, in Spain. The students, who had all undertaken an introductory course in Probability Theory, were tested through both written questionnaires and one-to-one interviews, where they were presented with situations that demanded the ability to apply the knowledge they had learnt, at a high level, to a range of situations and to justify their reasoning. The results show that the vast majority of students had a poor understanding of random phenomena, applying alternative ideas to the ones taught on their course in Probability. The need to improve teaching strategies in Probability and Statistics, so that students can develop skills in constructing probabilistic models, is highlighted.     

Dynamical effects of biocontrol on the ecosystem: Benefits or harm?

Motivated by recent field studies on the effects of biocontrol beetle on invasive plants (Tamarix) on riparian ecosystems, we develop a simple three-species (the native consumer, the biocontrol agent, and their predator) model to explore potential dynamical benefits and harm of introducing a non-indigenous species into varied ecosystems with different habitat structures. Our proposed model assumes that (1) habitat consists of both native plants that are main food resources of the native consumer and invasive plants which are targeted food resources of the biocontrol agents; (2) the habitat structure is stable which has a fixed ratio of invasive plants; (3) biocontrol agents can defoliate invasive plants whose defoliations provide as additional food resources for the native consumer that could potentially increase the native consumer’s abundance; and (4) the predators feed on both the native consumer and the biocontrol agents. Our study shows that introducing biocontrol agents into the ecosystem can generate complicated dynamics that could be beneficial or harmful to the ecosystem depending on the environments: biocontrol agents could be beneficial by promoting its biodiversity such that all species could coexist; on the other hand, biocontrol agents could also be harmful by eliminating the native consumer or the predator. In addition, biocontrol agents could stabilize or destabilize the ecosystem depending on the habit structure and the local ecological environments. These theoretical results provide us potential decision-making tools that allow managers to better predict both safety and efficacy of candidate biological control agents are needed.     

Is there chaos in the Spanish labour market?

One could argue that there is a resurgence of the non-linear modelling in economics. Some instruments have been developed to measure the complexity or instability of the analysed systems. At the present work some of these developed techniques are applied to verify the non-linearity present in the time series of Spanish unemployment, as well as to quantify the degree of complexity of the system that has generated the series. Using these techniques we find evidence of chaos in Spanish unemployment time series.     

Version Carleman du théorème de l'« edge of the wedge å

J.-P. Rosay has given a C^∞ version of “the edge of the wedge” theorem for non-smooth edges. We give now a “Carleman” version of this theorem, taking on one hand, an edge Rⁿ, and on the other hand, a C³ totally real submanifold of Cⁿ.     

The electoral system for the Italian Senate: an analogy with deterministic chaos?

The electoral system adopted for the allocation of seats in the Italian Senate utilizes a complex mechanism of awards at a regional level with the aim of strengthening, when necessary, the winning coalition and so improve overall government stability. The results presented here demonstrate that in a significant number of cases, the effect of the mechanism is opposite to that desired, to wit, weakening the resultant government by awarding more seats to the minority coalition. Indeed the award to the minority can even be such that the minority coalition becomes the majority and wins the election. The application of the award mechanism is strongly unpredictable as it depends crucially on the precise number of seats independently obtained in each region, and that each adjustment thereof can be positive, zero or negative; a characteristic that closely resembles the behaviour of a chaotic dynamical system whose trajectory, although purely deterministic, depends on infinitely precise details and is therefore unpredictable. To perform the systematic numerical analysis of the award effectiveness, we introduce characteristic polynomials, one for each electoral district, which carry information about all possible outcomes and award applications. Their product yields a polynomial containing the dependence of the result at national level on each of the regional awards.     

How to use the method of the improvising differentiation?

<正>We know the Substitution Rule,which is based on the following identity in differentiation.∫f(g(x))g′(x)dx=∫f(u)du(where u=g(x)).Now,we'll talk about how to use the method of the improvising differentiation,and give some examples by using basic     

How to use the Fundamental Theorem of Calculus?

Now we can put the two part of the Fundamental Theorem of Calculus together named the Fundamental Theorem of Calculus:Suppose f（x）is continuous on[a,b].1.If F（x）=∫₀^xf（t）dt,then F’（x）=f（x）.2.∫_α^bf（x）dx=F（b）-F（a）,where     

How to estimate the sum of a series?

<正>Now we’ll learn how to estimate the sum of a series?We have been able to use the integral test to show that a series ∞∑(n=1)a_n is convergent or divergent.But we also don’t know the best way to find the sum of the series.It is difficult to compute the sum of any series.Here is the best way to find an approximation to the sum of the series.You know     

Design Science,the design of systems and Operational Research: back to the future?

The relationship between the science of decision making and the design of systems that support or automate the decision-making process is vital to both academic and practical Operational Research (OR). There is a long-standing need to better understand how OR can be structured so as to contribute to the design of systems, rather than just the science of decisions. This paper articulates the notion of design-oriented OR, particularly within the context of IT-enabled systems, as one approach to addressing this issue. It proposes Design Science (DS) as one way of achieving design-oriented OR, and suggests a reference model for DS as a design-oriented approach to OR. The use and value of DS within the broader remit of management research, and differences with existing systems methodologies, are briefly considered. It concludes by noting that a DS approach would return OR, at least partially, to the values and approach of early OR practitioners, and hence back to the future.