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Quadtree-based partitioning (i.e., recursively dividing a picture into square blocks) is one of the most popular partitioning-based image coding schemes because of its computational simplicity and efficient representation of partitioning. However, the rate-distortion performance of quadtree-based partitioning reaches a limit because the dependence between child blocks of different parents is not exploited. In this paper, a new bottom-up-based block partitioning method called split-and-merge is proposed. This method splits an image into multiple square blocks and merges them into nonsquare blocks to exploit the dependence between split blocks. Moreover, a modification of the conventional intra prediction and transform is employed for nonsquare blocks. The experimental results indicate that the proposed method results in an average and maximum bit rate reduction of 3.1% and 8.3%, respectively, relative to High Efficiency Video Coding intra coding. [ABSTRACT FROM PUBLISHER]

We show that the major counting conjectures of modular representation theory are satisfied for 2-blocks of defect at most 4 except one possible case. In particular, we determine the invariants of such blocks. [ABSTRACT FROM AUTHOR]

The article focuses on how to understand fractions in which mathematics specialist Snider uses funky cookie tasks to teach fifth-grade students with mathematical concepts under the Virginia Mathematics and Science Coalition (VMSC). It mentions that the students participate in problem-solving which use drawings and manipulative to explore mathematical concepts in the elementary school curriculum. It says that the students assemble polygons by combining pattern blocks to understand the processes involved in converting improper fractions to mixed numbers.

This study investigated the use of block-building interventions to develop spatial-reasoning skills in kindergartners. Two intervention conditions and a control condition were included to determine, first, whether the block building activities themselves benefited children's spatial skills, and secondly, whether a story context further improved learning. Spatial measures included: spatial visualization, mental rotation, and block building. Results showed: for block building, interventions within a story context improved performance compared to the other two conditions. For spatial visualization, both types of block-building interventions improved performance compared to the control condition. Findings suggest: (1) storytelling provides an effective context for teaching spatial content, (2) teaching block building develops wider spatial skills, and (3) 3-dimensional mental rotation tasks show a male advantage in kindergartners. [ABSTRACT FROM AUTHOR]

Presents suggestions on the use of computers in teaching mathematics to elementary students. Attitude of a student toward a computer in the classroom; Overview of a geometric activity using bocks; Application of the activity in a computer.

The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got. [ABSTRACT FROM AUTHOR]

Focuses on the use of toy blocks for teaching geometric concepts to elementary school children. Mechanics for exploring shapes and investigating structures; Tips for solving problems and developing spatial sense; Exploration of properties of shapes using the blocks.

Describes a series of lessons which extend the concrete experiences that many elementary students have had with attribute blocks to provide middle shool students with information opportunities to explore the concepts and properties of relations and functions. How elementary students have been classified by the teaching profession; Highlights of the preliminary attribute-block activities used in these elementary classes.

Provides information on aids and devices for mathematics study and teaching. Benefits of using the DigiBlock Classroom Set in teaching mathematics; Features of the Fun Times card game.