Teachers and parents closely monitor students' progress in mathematics, recognizing its pivotal role in shaping their perspectives and unlocking diverse career opportunities. Despite extensive research aimed at enhancing mathematical achievement, certain factors remain crucial, notably mathematics anxiety and self-efficacy. This study investigates the interplay among these constructs, particularly focusing on the role of mathematics anxiety in mediating the relationship between math self-efficacy and overall mathematical performance among senior high school students. Involving 471 participants, this research employed a survey-based approach utilizing an adapted questionnaire. Correlation analysis revealed a significant association between math self-efficacy and academic achievement. Regression analysis further elucidated that mathematics anxiety serves as a partial mediator in this relationship. Notably, the findings suggest that reducing levels of math anxiety strengthens the positive influence of math self-efficacy on students' mathematical performance. These insights offer valuable implications for educational interventions aimed at fostering a supportive environment conducive to mathematical learning and achievement
Abstract We explore entanglement as a resource to distinguish locally indistinguishable orthogonal quantum states. Specifically, we consider sets which contain states from an unextendible product basis along with a pure entangled state. We establish a connection between the aforesaid problem and the entanglement-assisted discrimination of a certain class of many-copy indistinguishable sets. The entanglement-assisted protocols that we construct here are quite efficient, as they render the teleportation-based protocols sub-optimal. In fact, a central aspect of our study is to explore the role of Schmidt rank as a resource to distinguish the states of locally indistinguishable sets. Interestingly, we identify an instance where a set of locally indistinguishable orthogonal states remains locally indistinguishable even with access to any finite number of copies, yet becomes perfectly distinguishable using entangled resources of relatively low cost. This fact makes it possible to compare the degrees of local indistinguishability associated with several locally indistinguishable sets within the same Hilbert space. Consequently, we report a hierarchy of local indistinguishability among the many-copy indistinguishable sets. Thereafter, based on our analysis, we present a theoretical proposal for an information processing protocol exhibiting secure locking of information and its resource-efficient extraction. Furthermore, we also find that the hierarchical difference in local indistinguishability can increase with increasing dimension of the Hilbert space.
Combinatorics on words is a relatively recent and rich field that involves formal grammar, algebra, geometry, fractals, algorithms, and coding, with initial research focused on repetitions in words. In this paper, we measure the differences between patterns shared by words of the same length. We introduce word motifs to represent collections of words that share the same underlying patterns, and we generalize the Hamming distance for comparing word motifs. A word motif is an equivalence class of words of the same length over an alphabet under the equivalence relation induced by symbol relabeling. We study initial problems in comparing word motifs. We compute the maximal generalized Hamming distance for k word motifs of length n over an alphabet of ℓ symbols, and we demonstrate how to calculate the exact generalized Hamming distance between a pair of word motifs.
Enock Mulenga, Math H. J. Bollen, Nicholas Etherden
This paper presents a stochastic approach to single-phase and three-phase EV charge hosting capacity for distribution networks. The method includes the two types of uncertainties, aleatory and epistemic, and is developed from an equivalent method that was applied to solar PV hosting capacity estimation. The method is applied to two existing low-voltage networks in Northern Sweden, with six and 83 customers. The lowest background voltage and highest consumption per customer are obtained from measurements. It is shown that both have a big impact on the hosting capacity. The hosting capacity also depends strongly on the charging size, within the range of charging size expected in the near future. The large range in hosting capacity found from this study—between 0% and 100% of customers can simultaneously charge their EV car—means that such hosting capacity studies are needed for each individual distribution network. The highest hosting capacity for the illustrative distribution networks was obtained for the 3.7 kW single-phase and 11 kW three-phase EV charging power.
We present a simple and efficient MATLAB implementation of the local refinement for polygonal meshes. The purpose of this implementation is primarily educational, especially on the teaching of adaptive virtual element methods.
In this paper a semidiscrete Fourier pseudospectral method for approximating Benjamin-type equations is introduced and analyzed. A study of convergence is presented.
This research is concerned with finding the roots of a function in an interval using Chebyshev Interpolation. Numerical results of Chebyshev Interpolation are presented to show that this is a powerful way to simultaneously calculate all the roots in an interval.
Solving sparse recovery problem with high oversampling ratio is hard. We show that it is theoretically possible and we propose two modified HTP algorithms with such performances.
The paper gives an extension of Prony's method to the multivariate case which is based on the relationship between polynomial interpolation, normal forms modulo ideals and H--bases.
The Gasca-Maeztu conjecture for the case $n=4$ was proved for the first time in [J. R. Busch, A note on Lagrange interpolation in $\mathbb{R}^2$, Rev. Un. Mat. Argentina, 36 (1990) 33--38]. Here we bring a short and simple proof of it.
This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.