Geometric Achromatic and Pseudoachromatic Indices

The pseudoachromatic index of a graph is the maximum number of colors that can be assigned to its edges, such that each pair of different colors is incident to a common vertex. If for each vertex its incident edges have different color, then this maximum is known as achromatic index. Both indices have been widely studied. A geometric graph is a graph drawn in the plane such that its vertices are points in general position, and its edges are straight-line segments. In this paper we extend the notion of pseudoachromatic and achromatic indices for geometric graphs, and present results for complete geometric graphs. In particular, we show that for n points in convex position the achromatic index and the pseudoachromatic index of the complete geometric graph are \(\lfloor \frac{n^2+n}{4} \rfloor \).     

On the determination of approximate periodic solutions of some non-linear ODE

We propose a numerical-symbolic method for the approximation of periodic solutions of a type of non-linear ODE. The efficiency of our method is contrasted with the harmonic balance method and with another one which combines the differential transformation method with Padé approximants on a non trivial example: the relativistic oscillator. It is shown that our method is computationally more reliable.     

On generalized balanced optimization problems

In the generalized balanced optimization problem (GBaOP) the objective value \({\max_{e \in S}{|c(e)-k\max(S)|}}\) is minimized over all feasible subsets S of E = {1, . . . , m}. We show that the algorithm proposed in Punnen and Aneja (Oper Res Lett 32:27–30, 2004) can be modified to ensure that the resulting solution is indeed optimal. This modification is attained at the expense of increased worst-case complexity, but still maintains polynomial solvability of various special cases that are of general interest. In particular, we show that GBaOP can be solved in polynomial time if an associated bottleneck problem can be solved in polynomial time. For the solution of this bottleneck problem, we propose two alternative approaches.     

An investigation of assessment and feedback practices in fully asynchronous online undergraduate mathematics courses

Research suggests it is difficult to learn mathematics in the fully asynchronous online (FAO) instructional modality, yet little is known about associated teaching and assessment practices. In this study, we investigate FAO mathematics assessment and feedback practices in particular consideration of both claims and findings that these practices have a powerful influence on learning.

A survey questionnaire was constructed and completed by 70 FAO undergraduate mathematics instructors, mostly from the USA, who were each asked to detail their assessment and feedback practices in a single FAO mathematics course. Alongside these questions, participants also answered the 16-item version of the Approaches to Teaching Inventory. In addition, a novel feedback framework was also created and used to examine how feedback practices may be related to participants' approaches to teaching.

Results show that assessment and feedback practices are varied and complex: in particular, we found there was not a simple emphasis on summative assessment instruments, nor a concomitant expectation these would always be invigilated. Though richer assessment feedback appears to be emphasized, evidence suggests this feedback may not be primarily directed at advancing student learning. Moreover, we found evidence of a reliance on computer--human interactions (e.g. via computer-assisted assessment systems) and further evidence of a decline in human interactions, suggesting a dynamic that is both consistent with current online learning theory and claims FAO mathematics courses are becoming commodified. Several avenues for further research are suggested.     

Generalized asymptotic functions in nonconvex multiobjective optimization problems

In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.     

A functional analysis of NOx levels: location and scale estimation and outlier detection

This paper analyzes the NOx levels measured by a control station near a power plant by using techniques for functional data. First, we test for differences between the levels on working and non working days. Second, we obtain several location estimators and confidence sets of the center of the functional distribution. Third, we provide scale estimators and confidence sets of the dispersion of the functional distribution. Finally, a distance based procedure provides a criterion to determinate the presence of outlying observations, which allows to detect relevant NOx levels.     

The Piracicaba River basin: isotope hydrology of a tropical river basin under anthropogenic stress

The stable isotope content of samples of precipitation and of the river water throughout the Piracicaba basin in Brazil was measured over a two-year period. The isotope values of precipitation follow a consistent pattern of relatively depleted values of both deuterium and oxygen 18 during the rainy summers and enriched ones during the dry winters, with all values aligned slightly above the Global Meteoric Water Line. The isotopic composition of the river water throughout the basin shows a remarkable spatial coherence and much smaller scatter of data than those of the precipitation. The isotope composition of river water is close to that of the precipitation in the rainy season, however, with a consistent lower d-excess value by 1/1000-2/1000. This is attributed to evaporative water loss in the basin, in part an expression of the recycling of water due to the anthropogenic activity in the region. The more divergent values are recorded during high-water stages in the rivers. In many cases, the floods during the beginning of the rainy season are characterized by an enrichment of the heavy isotopes and lower d-excess values when compared to the precipitation, with the opposite situation later in the rainy season. This is interpreted as resulting from the watershed/riverflow interaction pattern, and it thus suggests that the isotope composition can monitor the hydrologic situation in the basin and its changes.     

Proton conduction in the binary system (1 − x)CsHSeO4–xKHSeO4 studied with a free-energy model

Electrical Impedance Spectroscopy (EIS) was used to study the electrical properties of the (1???x)CsHSeO₄–xKHSeO₄ binary system with concentrations x?=?0.0 and 0.1. The results show a higher proton-conduction phase above 80°C for both concentrations, however, while DC conductivity of CsHSeO₄ shows a gradual change to higher values in the 80–118°C temperature range, the 0.9CsHSeO₄–0.1KHSeO₄ concentration reveals an abrupt change at about 80°C to an intermediate temperature phase. The observed behavior for the doped sample was modeled using a trial free-energy density, based on the concentration of mobile ions, that takes into account the formation of defects, configurational and phonon entropies, and defect-defect interactions. By minimising the free-energy density one obtains two roots for the carrier concentration at a given temperature, which corresponds to a stable and metastable configuration. It is possible to characterise the phase behavior of the system by means of temperature and two model parameters, which depend on the crystalline properties of the system, but not on temperature. One can successfully explain the conductivity behavior of the system by changing the model parameters if it is assumed that its variations are due to the carriers density.