3-Total Edge Product Cordial Labeling for Stellation of Square Grid Graph

Let G be a simple graph with vertex set V G and edge set E G . An edge labeling δ : E G ⟶ 0,1 , … , p − 1 , where p is an integer, 1 ≤ p ≤ E G , induces a vertex labeling δ ∗ : V H ⟶ 0,1 , … , p − 1 defined by δ ∗ v = δ e 1 δ e 2 ⋅ δ e n mod p , where e 1 , e 2 , … , e n are edges incident to v . The labeling δ is said to be p -total edge product cordial (TEPC) labeling of G if e δ i + v δ ∗ i − e δ j + v δ ∗ j ≤ 1 for every i , j , 0 ≤ i ≤ j ≤ p − 1 , where e δ i and v δ ∗ i are numbers of edges and vertices labeled with integer i , respectively. In this paper, we have proved that the stellation of square grid graph admits a 3-total edge product cordial labeling.

Configurable pixelated skyrmions on nanoscale magnetic grids

Topological spin textures can serve as non-volatile information carriers. Here we study the current-induced dynamics of an isolated magnetic skyrmion on a nanoscale square-grid pinning pattern formed by orthogonal defect lines with reduced magnetic anisotropy. The skyrmion on the square grid can be pixelated with a quantized size of the grid. We demonstrate that the position, size, and shape of skyrmion on the square grid are electrically configurable. The skyrmion center is quantized to be on the grid and the skyrmion may show a hopping motion instead of a continuous motion. We find that the skyrmion Hall effect can be perfectly prohibited due to the pinning effect of the grid. The pixelated skyrmion can be harnessed to build future programmable racetrack memory, multistate memory, and logic computing device. Our results will be a basis for digital information storage and computation based on pixelated topological spin textures on artificial pinning patterns.

Efektivitas Media Tangram Berpetak Terhadap Hasil Belajar Matematika Siswa Sekolah Dasar

This study aims to determine the effect of square-grid tangram media on student learning result, especially on polygon material. This research is a quasi-experimental study with the design of one group pre-test post-test conducted at one of the Elementary Schools in Bandung Regency. The samples from this study were 32 students with learning using square-grid tangram media. The data was processed with the help of IBM SPSS version 26. The test steps are 1) The Normality Test, and 2) T-Test. The conclusions of this study are 1) Achieving the ability of students in many facets using tangram media better, 2) The use of tangram media is more effective when used in polygon material, 3) Students more quickly understand the material and students feel motivated.

A Reusable Efficient Green Catalyst of 2D Cu-MOF for the Click and Knoevenagel Reaction

[Cu(CPA)(BDC)]n (CPA = 4-(Chloro-phenyl)-pyridin-4-ylmethylene-amine; BDC = 1,4-benzenedicarboxylate) has been synthesized and structurally characterized by single crystal X-Ray diffraction measurement. The structural studies establish the copper (II) containing 2D sheet with (4,4) square grid structure. The square grid lengths are 10.775 and 10.769 Å. Thermal stability is assessed by TGA, and subsequent PXRD data establish the crystallinity. The surface morphology is evaluated by FE-SEM. The N2 adsorption−desorption analysis demonstrates the mesoporous feature (∼6.95 nm) of the Cu-MOF. This porous grid serves as heterogeneous green catalyst with superficial recyclability and thermal stability and facilitates organic transformations efficiently such as, Click and Knoevenagel reactions in the aqueous methanolic medium.

Application of GIS Tools in the Measurement Analysis of Urban Spatial Layouts Using the Square Grid Method

The principal aim of this paper is to present the capabilities of newly developed GIS tools for measurement analysis of urban spatial layouts, using the square grid method. The study of urban morphology and metrology is a multistage process, which involves the metrological analysis of town plans. The main research step is the determination of measurement modules of town layouts, using the square grid. By using GIS software, the authors developed a new tool, named HGIS Tools, which allow to create any number of modular grids with the selected cell size that corresponds to urban units of distance and surface area. When investigating a large number of towns and cities, this offers a significant improvement of the research procedure. The paper presents a test of the tool’s potential on the example of regular medieval towns from the area of the former Teutonic Order state (currently the territory of Poland), diversified in terms of size, genesis and morphometrics. The obtained results confirmed that HGIS Tools allowed to determine the hypothetical measurement module of the layout of the cities studied. The results were consistent with the analyses of other authors carried out with the traditional grid-square methods. The test of the HGIS Tools showed their significant potential in conducting morphometric analyses of spatial arrangements of urban spatial layout on a larger scale.

A Dynamical System Approach to Polyominoes Generation*

We describe a method which exploits discrete dynamical systems to generate suitable classes of polyominoes. We apply the method to design an algorithm that uses O(n) space to generate in constant amortized time all polyominoes corresponding to hole-free partially directed animals consisting of n sites on the square grid. By implementing the algorithm in C++ we have obtained a new sequence that does not appear in the On-Line Encyclopedia of Integer Sequences.