Turbulence modeling from a new perspective

In this work we establish a link between a Reynolds averaged turbulence modeling methodology, containing interactions up to the second order correlations between the velocity fluctuations at various scales, and a multi-objective optimization problem with the constraints expressed in terms of equality and inequality, imposed by the given boundary conditions and the positive semi-definiteness of the Reynolds stress tensor, etc. The information unavailability and uncertainty associated with the boundary conditions for the fluctuation correlations of various orders is delineated, and the information from the Navier–Stokes equations is utilized to the extent allowed by the available input data necessary for simulations; turbulence from the perspective of systems simulation is explored and some objective functions are proposed. Finally, the challenges faced by the formulation and the issues yet to be resolved are discussed.     

On the use of integral transform methods: a new perspective

Integral transforms are usually used to ‘solve’ renewal‐type equations. These transforms typically require inversion to be of use to a decision maker. In this paper it is demonstrated that in certain situations, stochastic quantities of interest are expressible in terms of integral transforms, thus avoiding the problems associated with inversion.     

SAT graph-based representation: A new perspective

In this paper a new graph based representation of Boolean formulas in conjunctive normal form (CNF) is proposed. It extends the well-known graph representation of binary CNF formulas (2-SAT) to the general case. Every clause is represented as a set of (conditional) implications and encoded with different edges labeled with a set of literals, called context. This representation admits many interesting features. For example, a path from the node labeled with a literal ¬x to the node labeled with a literal x gives us an original way to compute the condition under which the literal x is implied. Using this representation, we show that classical resolution can be reformulated as a transitive closure on the generated graph. Interestingly enough, using the SAT graph-based representation three original applications are then derived. The first one deals with the 2-SAT strong backdoor set computation problem, whereas in the second one the underlying representation is used to derive hard SAT instances with respect to the state-of-the-art satisfiability solvers. Finally, a new preprocessing technique of CNF formulas which extends the well-known hyper-resolution rule is proposed. Experimental results show interesting improvements on many classes of SAT instances taken from the last SAT competitions.     

The compact-open topology: A new perspective

This paper studies the compact-open topology on the set KC(X) of all real-valued functions defined on a Tychonoff space, which are continuous on compact subsets of X. In addition to metrizability, separability and second countability of this topology on KC(X), various kinds of topological properties of this topology are studied in detail. Actually the motivation for studying the compact-open topology on KC(X) lies in the attempt of having a simpler proof for the characterization of a completeness property of the compact-open topology on C(X), the set of all real-valued continuous functions on X.     

Branching in the {\Sigma^0_2} -enumeration degrees: a new perspective

We give an alternative and more informative proof that every incomplete -enumeration degree is the meet of two incomparable -degrees, which allows us to show the stronger result that for every incomplete -enumeration degree a, there exist enumeration degrees x ₁ and x ₂ such that a, x ₁, x ₂ are incomparable, and for all b  ≤  a, b  =  (b ∨ x ₁ ) ∧ (b ∨ x ₂ ). The first author would like to thank her advisor, Andrea Sorbi, whose guidance made this paper possible. The second author has been supported by a Marie Curie Incoming International Fellowship of the European Community FP6 Program under contract number MIFI-CT-2006-021702.     

Images of mathematicians: a new perspective on the shortage of women in mathematical careers

Though women earn nearly half of the mathematics baccalaureate degrees in the United States, they make up a much smaller percentage of those pursuing advanced degrees in mathematics and those entering mathematics-related careers. Through semi-structured interviews, this study took a qualitative look at the beliefs held by five undergraduate women mathematics students about themselves and about mathematicians. The findings of this study suggest that these women held stereotypical beliefs about mathematicians, describing them to be exceptionally intelligent, obsessed with mathematics, and socially inept. Furthermore, each of these women held the firm belief that they do not exhibit at least one of these traits, the first one being unattainable and the latter two being undesirable. The results of this study suggest that although many women are earning undergraduate degrees in mathematics, their beliefs about mathematicians may be preventing them from identifying as one and choosing to pursue mathematical careers.     

Orthogonal regression: a teaching perspective

A well-known approach to linear least squares regression is that which involves minimizing the sum of squared orthogonal projections of data points onto the best fit line. This form of regression is known as orthogonal regression, and the linear model that it yields is known as the major axis. A similar method, reduced major axis regression, is predicated on minimizing the total sum of triangular areas formed between data points and the best fit line. Either of these methods is appropriately applied when both x and y are measured, a typical case in the natural sciences. In comparison to classical linear regression, equation derivation for the slope of the major axis and reduced major axis lines is a nontrivial process. For this reason, derivations are presented herein drawing from previous literature with as few steps as possible to enable an easily accessible understanding. Application to eruption data for Old Faithful geyser, Yellowstone National Park, Wyoming and Montana, USA enables a teaching opportunity for choice of model.     

Routing problems: a historical perspective

This paper presents an historical perspective on routing problems. Today a well-established class of optimization problems, routing problems have played a pivotal role in the development of Logistics as a discipline, even influencing other sectors not directly connected to management studies. The aim of this paper is to provide an overview of the evolution of this topic, starting from seminal contributions by Euler and Hamilton, and illustrating the most recent applications. This article is based on a longer article originally published in Italian (Bruno et al. 2010 Bruno, G, Genovese, A, Improta, G, ‘Storia dei problemi di routing, da Eulero ai nostri giorni’, in Proceedings of the 3rd Italian Conference on Engineering History (in Italian), 2010  [Google Scholar]).     

Robust convex optimization: A new perspective that unifies and extends

Mathematical Programming - Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new...     

Fractal regularities of sub-harmonic motions perspective for pulse dynamics monitoring

The pulse energy conversion systems demonstrate a complex dynamics at parameter variations in a wide range. The problem of one-to-one decision-making about system dynamics using a priori information in the form of the parameter diagram is considered. The step-by-step approach to the problem solution based on fractal regularities of the dynamics is proposed. The first stage is the type of motion identification; the second one is the parameter vector identification within this motion type. The parallel and sequential algorithm schemes for this approach realization are presented. The problem of dynamics evolution forecasting is suggested to consider as a pointer to future research.     

A new perspective on k-triangulations

We connect k-triangulations of a convex n-gon to the theory of Schubert polynomials. We use this connection to prove that the simplicial complex with k-triangulations as facets is a vertex-decomposable triangulated sphere, and we give a new proof of the determinantal formula for the number of k-triangulations.     

Solving mathematical problems: a personal perspective

Feel like writing a review for The Mathematical Intelligencer? You are welcome to submit an unsolicited review of a book of your choice; or, if you would welcome being assigned a book to review, please write us, telling us your expertise and your predilections.     

Convoy movement problem: a civilian perspective

We study the convoy movement problem in peacetime from a civilian perspective by seeking to minimize civilian traffic disruptions. We develop an exact hybrid algorithm that combines the k-shortest path algorithm along with finding a minimum weighted k-clique in a k-partite graph. Through this coupling scheme, we are able to exactly solve large instances of the convoy movement problem without relaxing many of its complicating constraints. An experimental study is performed based on pseudo-transportation networks to illustrate the computational viability of the method as well as policy implications.     

Revisiting decimal misconceptions from a new perspective: The significance of whole number bias in the Chinese culture

The aim of this study was to investigate Hong Kong Grade 4 students’ understanding of the decimal notation system including their knowledge of decimal quantities. This is a unique study because most previous studies were conducted in Western cultural settings; therefore we were interested to see whether Chinese students have the same kinds of misconceptions as Western students given the Chinese number naming system is relatively transparent and explicit. Three hundred and forty-one students participated in a written test on decimal numbers. Thirty-two students were interviewed to further explore their mathematical reasoning. In summary, the results indicated that many students had mastered reasonable knowledge of decimal notation and quantities, which may be attributed to the Chinese linguistic clarity of decimal numbers. More importantly, the results showed that some students’ construction of decimal concepts have been adversely affected by persistent misconceptions arising from whole number bias. Two kinds of whole number misconceptions, namely “-ths suffix error” and “reversed place value progression error”, were revealed in this study. This paper suggests that a framework theory approach to conceptual change may be an alternative approach to addressing students’ learning difficulties in decimals.     

A new perspective on implementation by voting trees

Voting trees describe an iterative procedure for selecting a single vertex from a tournament. They provide a very general abstract model of decision‐making among a group of individuals, and it has therefore been studied which voting rules have a tree that implements them, i.e., chooses according to the rule for every tournament. While partial results concerning implementable rules and necessary conditions for implementability have been obtained over the past 40 years, a complete characterization of voting rules implementable by trees has proven surprisingly hard to find. A prominent rule that cannot be implemented by trees is the Copeland rule, which singles out vertices with maximum degree. In this paper, we suggest a new angle of attack and re‐examine the implementability of the Copeland solution using paradigms and techniques that are at the core of theoretical computer science. We study the extent to which voting trees can approximate the maximum degree in a tournament, and give upper and lower bounds on the worst‐case ratio between the degree of the vertex chosen by a tree and the maximum degree, both for the deterministic model concerned with a single fixed tree, and for randomizations over arbitrary sets of trees. Our main positive result is a randomization over surjective trees of polynomial size that provides an approximation ratio of at least 1/2. The proof is based on a connection between a randomization over caterpillar trees and a rapidly mixing Markov chain. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 59–82, 2011     

Minimum standards for investment performance: A new perspective on non-life insurer solvency

The aim of this paper is to develop an alternative approach for assessing an insurer’s solvency as a proposal for a standard model for Solvency II. Instead of deriving minimum capital requirements–as is done in solvency regulation–our model provides company-specific minimum standards for risk and return of investment performance, given the distribution structure of liabilities and a predefined safety level. The idea behind this approach is that in a situation of weak solvency, an insurer’s asset allocation can be adjusted much more easily in the short term than can, for example, claims cost distributions, operating expenses, or equity capital. Hence, instead of using separate models for capital regulation and solvency regulation–as is typically done in most insurance markets–our single model will reduce the complexity and costs for insurers as well as for regulators. In this paper, we first develop the model framework and second test its applicability using data from a German non-life insurer.     

Multiple criteria decision aiding: a dialectical perspective

This is a summary of the Ouerdane’s PhD thesis supervised by Alexis Tsoukiàs and Nicolas Maudet and defended on 01 December 2009 at the Université Paris-Dauphine, Paris. The thesis is written in English and is available from the author upon request. This work has the aim to investigate the different ways to use argumentation theory in a decision context. More precisely within multi-criteria evaluation models. The principal aim is to meet the needs in terms of explanations and revision during a decision process.     

Problem solving: a personal perspective from Brazil

In this paper, I do a historical review of the concept of Problem Solving, and make some considerations about the State of the Art nowadays. A very brief notice of the art of Problem Solving in Latin America is also presented. Finally, I present some reflections on the future of the Art of Problem Solving.