Examining 4th Grade Gifted and Non-Gifted Students Understanding Levels of Place Value

The aim of this research is to reveal the understanding of dimensions and sub-dimensions of the place value in natural numbers of gifted and non-gifted students attending fourth grade. A mixed approach was adopted in the research. The research is quantitative in terms of revealing the levels of place value, counting, representing, naming, renaming, comparing and calculating the dimensions of the students and comparing the general mean score of both groups with the mean score for each dimension, and it is qualitative in terms of revealing the mistakes made in these dimensions. The study group of the research consists of 76 students diagnosed as gifted who attend four different SACs and 90 non-gifted fourth grade students attending in a regular school in town in the Central Anatolia Region. According to the findings obtained in the research, it was revealed that students with a diagnosis of giftedness could not reach the desired learning level in the count by 10 forward sub-dimension of the counting dimension of the place value. It was also revealed that they could not reach the desired learning level in the non-standard representation sub-dimension of the representation dimension. On the other hand the non-gifted students could not reach the desired learning level also in the division sub-dimension of the calculation dimension. It was concluded that students that are diagnosed as gifted had high success in terms of understanding the place value of natural numbers. For both groups of students, it can be said that they have difficulties in operations with non-standard representations, and they have difficulty in thinking differently because they are used to doing the questions by memorization and rules. Experimental studies can be carried out on the dimensions of the place value.

Algorithms of multidimensional random process simulation

The article discusses two approaches to modeling signals and processes: the method of filter construction and the trigonometric method. It is shown that the later approach is more promising, since an increase in the signal/process representation dimension mathematically means adding a term to the basis function formula, which gives access to fast simulation algorithms. Examples of algorithms for multidimensional simulation of random processes using two methods are given and a software system that implements these algorithms is described. The results provided by the software system will allow you to predict characteristics of engineering projects (accuracy and speed of modeling algorithms). Due to the high relevance of and need for fundamental research of methods and algorithms for digital transformation of the component base, the digitalization of all aspects of activity, including the synthesis of new materials, the development of new methods for designing micro- and nano-systems, the article aims to expand the scope of the spectral method of simulating multidimensional processes using original algorithmic complexes.

On representation dimension of tame cluster tilted algebras

The aim of this work is to study the representation dimension of cluster tilted algebras. We prove that the weak representation dimension of tame cluster tilted algebras is equal to three. We construct a generator module that reaches the weak representation dimension, unfortunately this module is not always a cogenerator. We show for which algebras this module gives the representation dimension.

Gabriel–Roiter Measure, Representation Dimension and Rejective Chains

The Gabriel–Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel–Roiter measure can be extended to abelian length categories and every such category has multiple Gabriel–Roiter measures. Using this notion, we prove the following broader statement: given any object $X$ and any Gabriel–Roiter measure $\mu$ in an abelian length category $\mathcal{A}$, there exists an object $X^{\prime}$ that depends on $X$ and $\mu$, such that $\Gamma =\operatorname{End}_{\mathcal{A}}(X\oplus X^{\prime})$ has finite global dimension. Analogously to Iyama’s original results, our construction yields quasihereditary rings and fits into the theory of rejective chains.

Neural Representations of Abstract Concepts: Identifying Underlying Neurosemantic Dimensions

The abstractness of concepts is sometimes defined indirectly as lacking concreteness, this view provides little insight into their cognitive or neural basis. Multivariate pattern analytic techniques applied to functional magnetic resonance imaging data were used to characterize the neural representations of 28 individual abstract concepts. A classifier trained on the concepts’ neural signatures reliably decoded their neural representations in an independent subset of data for each participant. There was considerable commonality of the neural representations across participants as indicated by the accurate classification of each participant’s concepts based on the neural signatures obtained in other participants. Group-level factor analysis revealed 3 semantic dimensions underlying the 28 concepts, suggesting a brain-based ontology for this set of abstract concepts. The 3 dimensions corresponded to 1) the degree a concept was Verbally Represented; 2) whether a concept was External (or Internal) to the individual, and 3) whether the concept contained Social Content. Further exploration of the Verbal Representation dimension suggests that the degree a concept is verbally represented can be construed as a point on a continuum between language faculties and perceptual faculties. A predictive model, based on independent behavioral ratings of the 28 concepts along the 3 factor dimensions, provided converging evidence for the interpretations.