New Definition of Ultrafine Particles in Mine Paste and Its Relationship with Rheological Properties

Mine backfill paste is generally composed of tailings and coarse aggregates. In engineering practice, the definitions in fill material classification are vague. In this paper, the size range of ultrafine particles is defined by the Stokes sedimentation test and hydraulic coarseness method. The size range of ultrafine particles is affected not only by the geometric size of the particles but also by the physical characteristics of the particles themselves. This definition has more comprehensive considerations and stricter physical and mathematical significance than the traditional definition of ultrafine particles based only on size. There is a strong correlation between ultrafine particles in fill materials and the rheological properties of the mine backfill paste. In this study, through experiments and correlation analysis, it was found that the content of ultrafine particles is positively correlated with the plastic viscosity of the mine backfill paste, and its growth range is exponential. The coarse aggregate content is positively correlated with the yield stress of the mine backfill paste. A regression analysis model was established for the rheological properties of mine backfill paste. The model has few factors and high correlation, so it can simply and efficiently predict the rheological properties of mine backfill paste and guide engineering practice.

Modeling of neutron flux density anomalies in the automated system of «Shelter» Object’s nu-clear safety control.

Analysis of the dynamics of neutron flux density (NFD) from fuel-containing masses (FCM) in the «Shelter» Object shows the presence of values that exceed the average values for different observation periods. Identification of such values by the criterion of «anomaly / non-anomaly» will allow excluding uninformative events from the array of observations. Or, in the case of the anomaly confirmation, it will allow forming effective actions for decision-making in order to eliminate the consequences of such events. To solve the problem of detecting anomalous measurements, now there is utilized the theory of statistical solutions which is based on the use of parametric methods. The utilization of these methods requires a priori information about the nature of the distribution of the measured process and its parameters. In order to find an effec-tive solution to the problem of detecting and eliminating anomalous measurements, it is necessary to know the statistical characteristics of normal and anomalous components. This paper proposes statistical criteria for estimating anomalies in time series of NFD which have different approaches to the formation of observation intervals, power and reliability of anomaly detection. Depending on the type of distribution of the array of observations, a set of criteria is proposed. These criteria are most expedient to use when checking the anomaly of series levels for the exponential distribution, the Poisson and Weibull distribution. The capacity of the criteria has been evaluated depending on the sample size. The article defines the accuracy of determination of anomalies by criteria with the known values of the mean and dispersion in the studied sample. As the result, it is recommended to use the Grubbs test to study the anomaly of the sample levels with n>700, and the Dixon and Smolyak-Titarenko criteria for the samples with n<50. The utilization of optimal criteria depending on the characteristics of the studied samples will increase the mathematical significance of the obtained results and, as a result, will improve the quality of management decisions and nuclear safety on the «Shelter» Object as a whole.

Adinkra Mathematics: A study of Ethnocomputing in Ghana

<div><p>This paper details the development and evaluation of software that allows middle school students to explore the mathematical aspects of Ghanaian Adinkra symbols. We tested the effectiveness of this simulation in a Ghanaian junior high school by conducting a randomized quasi-experiment. We begin this paper by framing culturally responsive math education within the interventionist tradition of ethnomathematics. We draw this tradition together with an empirical exploration of the mathematics embedded in Adinkra symbols. We follow this with a methodological explanation for how we translated the mathematical significance of Adinkra into the design of our software, “Culturally Situated Design Tools.” Finally, we describe the quasi-experimental evaluation of the software using a randomized assignment of students in control and intervention groups in Ghana. We found statistically significant improvement for students using the culture-based software in comparison to similar software with no cultural content.</p></div>

Interpreting the Standard Division Algorithm in a Candy Factory Context

In our mathematics courses for preservice elementary school teachers, we spend a good deal of time helping students make sense of the standard algorithms for whole-number operations. Our goal in focusing on “why the algorithms work” is not to suggest that teachers show children the algorithms and then tell them why they work. Rather, our goal is to promote a deeper understanding of the mathematical concepts underlying the algorithms. We believe that by making the routine problematic and challenging our students to think about the mathematical significance of the steps in the algorithms, they will be better prepared to respond to the multitude of ideas children bring to arithmetical computation.

The mathematical significance of proof theory

Returning to old ideas of Kreisel, I discuss how the mathematics of proof theory, often combined with tricks of the trade, can occasionally be useful in extracting hidden information from informal proofs in various areas of mathematics.

LONG DISTANCE PHYSICS OF THE HALL FLUID AND THE ANYON SUPERFLUID

The long distance physics of the Hall fluid and the anyon superfluid may be described by effective field theories constructed out of the Chern-Simons term. These theories are topological in character and may be of deep mathematical significance. Various physical quantities such as the quantum numbers of the quasiparticles are determined by a matrix appearing in the Chern-Simons term.

On the Mathematical Significance of the Similarity Index of Ochiai as a Measure for Biogeographical Habitats

A recent survey of similarity indices by Hubalek has shown that the index due to Ochiai is one of the few satisfying rather stringent conditions. It is shown that the Ochiai index has a geometrical interpretation that can be exploited to yield a critical value for separability of two habitats on the basis of their avifauna. This critical value is used to analyse data on bird habitats and is compared with the results of a null hypothesis test on the data. In addition, use is made of the indices of Jaccard and Sokal & Michener. When the null test is used at the 5% level, all three indices agree in separating the habitats. The presence of a critical value of the Ochiai index gives it an advantage. A table of critical values is given for various numbers of species.