From culture to well-being: a partial story of values in mathematics education

This article describes the growth of the idea of values in the field of mathematics education. The story of that development is however a personal one, as befits the topic of values, which themselves are highly personal. Instead of reporting a thorough literature search and account, the aim is to present an account as seen from the perspective of a researcher who is, and has been always, involved in the search for more productive ways to conceptualise mathematics education. The article thus sets the scene for the more scholarly foci of the articles in this collection.     

An evolution model of behavior and nash equilibria in game interactions

Translated from Programmnoe Obespechenie i Modeli Sistemnogo Analiza, pp. 71–78, 1991.     

Conformal field theories: From old to new

We discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. As an example, we discuss the new spin-2 gauged sigma models that arise from the general conformal nonlinear sigma model. We offer this contribution in memory of Dr. F. A. Lunev. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 117, No. 2, pp. 221–226, November, 1998     

Asymptotic behavior and blow-up of solutions to a nonlinear evolution equation of fourth order

In this paper, the asymptotic behavior of the solution to the initial–boundary value problem for a nonlinear evolution equation of fourth order

equation(1)

_utt−_a1uxx−_a2uxxt−_a3uxxtt=φ_(ux)x$u_{tt}-a_1{u}_{xx}-a_2{u}_{xxt}-a_3{u}_{xxtt}=\phi {\left(u_x\right)}_x$

is studied. The sufficient conditions for blow-up of the solutions to the initial–boundary value problems for Eq. (1) are given.     

From simulated annealing to stochastic continuation: a new trend in combinatorial optimization

Simulated annealing (SA) is a generic optimization method that is quite popular because of its ease of implementation and its global convergence properties. However, SA is widely reported to converge very slowly, and it is common practice to allow extra freedom in its design at the expense of losing global convergence guarantees. A natural way to increase the flexibility of SA is to allow the objective function and the communication mechanism to be temperature-dependent, the idea being to gradually reveal the complexity of the optimization problem and to increase the mixing rate at low temperatures. We call this general class of annealing processes stochastic continuation (SC). In the first part of this paper, we introduce SC starting from SA, and we derive simple sufficient conditions for the global convergence of SC. Our main result is interesting in two respects: first, the conditions for global convergence are surprisingly weak—in particular, they do not involve the variations of the objective function with temperature—and second, exponential cooling makes it possible to be arbitrarily close to the best possible convergence speed exponent of SA. The second part is devoted to the application of SC to the problem of producing aesthetically pleasing drawings of undirected graphs. We consider the objective function defined by Kamada and Kawai (Inf Process Lett 31(1):7–15, 1989), which measures the quality of a drawing as a weighted sum of squared differences between Euclidean and graph-theoretic inter-vertex distances. Our experiments show that SC outperforms SA with optimal communication setting both in terms of minimizing the objective function and in terms of standard aesthetic criteria.     

An evolution variational inequality related to a diffusion-absorption problem

An implicit non-steady free boundary problem is transformed into a variational inequality, which is solved by means of a semi-discretization technique.     

The role of culture in the emergence of decision‐making roles: An example using cultural algorithms

Cultural algorithms employ a basic set of knowledge sources, each related to knowledge observed in various animal species. These knowledge sources are then combined to direct the decisions of the individual agents in solving optimization problems. Here, the authors develop an algorithm based on an analogy to the marginal value theorem in foraging theory to guide the integration of these different knowledge sources to direct the agent population. The algorithm is applied to find the optimum in a dynamic environment composed of mobile resource cones. It is demonstrated that certain phases of problem solving emerge along with related individual roles during the solution process. © 2007 Wiley Periodicals, Inc. Complexity, 2008     

From a projective invariant to some new properties of algebraic hypersurfaces

Projective invariants are not only important objects in mathematics especially in geometry,but also widely used in many practical applications such as in computer vision and object recognition. In this work,we show a projective invariant named as characteristic number,from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property,two high-dimensional generalizations of Pascal's theorem are given,one establishing the connection of hypersurfaces of distinct degrees,and the other concerned with the intersections of a hypersurface and a simplex.     

Asymptotic behavior of a class of nonlinear evolution equations

In this paper, using a new method (or technology), we prove the existence and upper semi-continuity of the global attractors A_ω for a class of nonlinear evolution equations in D(A)×D(A), where the nonlinear term f satisfies a critical exponential growth condition.     

Integrated spatial assessment: a multicriteria approach to sustainable development of cultural and environmental heritage in San Marco dei Cavoti,Italy

Starting from the concept of “territory” and from the definition of “integrated assessment”, the paper defines the operational dimensions of spatial integrated assessment (ISA), applying it to the territorial context of San Marco dei Cavoti (a rural village in Southern Italy). In particular, the paper proposes an integration between analytic hierarchy process (AHP) and geographic information system (GIS) for the strategies definition of planning choices, recognizing the relevant role of the environmental aspects in the decision-making process and alternatives selection.      

Asymptotic behavior of bounded solutions to a nonhomogeneous second-order evolution equation of monotone type

By using previous results of Djafari Rouhani [B. Djafari Rouhani, Ergodic theorems for nonexpansive sequences in Hilbert spaces and related problems, Ph.D. Thesis, Yale university, 1981, part I, pp. 1-76; B. Djafari Rouhani, Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces, J. Math. Anal. Appl. 147 (1990) 465-476; B. Djafari Rouhani, Asymptotic behaviour of almost nonexpansive sequences in a Hilbert space, J. Math. Anal. Appl. 151 (1990) 226-235] for dissipative systems, we study the asymptotic behavior of solutions to the following system of second-order nonhomogeneous evolution equations:

     

A fuzzy approach to value and culture assessment and an application

This paper presents a fuzzy approach to the identification of organizational values and culture. The proposed approach has been developed from crisp assessment methods in the literature and has been applied to the Industrial Engineering Department (IED) at a state university in Turkey. Highly subjective judgments and ambiguity regarding the presence of values and the culture type of the organization resulting from these values suggest the necessity of using a fuzzy approach. Where the uncertainty arises from the inability to perform adequate measurements, fuzzy sets provide a mathematical method of representing such uncertainties. Applying the fuzzy approach, organizational values which are common, and should be common in the IED, are identified and these values are organized into four generic culture types – adhocracy culture, market culture, clan culture and hierarchy culture – stating in which culture type the IED belongs. Finally the uncertainties of the culture sets are quantified by the measure of fuzzy entropy.     

Asymptotic behavior of solutions: An application to stochastic NLP

In this article we study the consistency of optimal and stationary (KKT) points of a stochastic non-linear optimization problem involving expectation functionals, when the underlying probability distribution associated with the random variable is weakly approximated by a sequence of random probability measures. The optimization model includes constraints with expectation functionals those are not captured in direct application of the previous results on optimality conditions exist in the literature. We first study the consistency of stationary points of a general NLP problem with convex and locally Lipschitz data and then apply those results to the stochastic NLP problem and stochastic minimax problem. Moreover, we derive an exponential bound for such approximations using a large deviation principle.

     

Asymptotic behavior of solution to nonlinear evolution equations with damping

In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects

(E)