The Principle of Mathematical Induction: Applications in Physical Optics by Joseph Ivin Thomas

“…In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. In theoretical computer science, it bears the pivotal role of developing the appropriate cognitive skills necessary for the effective design and implementation of algorithms, assessing for both their correctness and complexity. …”
Get full text

s-Goodness for Low-Rank Matrix Recovery by Lingchen Kong, Levent Tunçel, Naihua Xiu

Get full text

Amplification of factors of regional markets transformations in the context of generation theory by R. S. Blizkiy, E. A. Divaeva

“…The researchers propose to consider combinatorics of the generations theory factors within the framework of Russian regional markets development. …”
Get full text

On a problem of Nathanson related to minimal asymptotic bases of order $h$ by Chen, Shi-Qiang, Sándor, Csaba, Yang, Quan-Hui

Get full text

Optimasi Rute Rencana Perjalanan Pesawat Menggunakan Algoritma Late Acceptance Hill Climbing (Studi Kasus : Travelling Salesman Challenge 2.0) by Ahmad Muklason, I Gusti Agung Premananda

“…Abstract The Traveling Salesman Problem (TSP) is a classic problem that is popularly researched in the field of combinatorics optimization. This problem aims to determine the shortest travel route to visit each location exactly once and, at the end of the trip, must return to where the trip started. …”
Get full text

The Singularity of the <i>K</i>₄ Homeomorphic Graph by Haicheng Ma

“…The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. For positive integers <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mn>6</mn></mrow></semantics></math></inline-formula>. …”
Get full text

The GeoTox Package: open-source software for connecting spatiotemporal exposure to individual and population-level risk by Kyle P. Messier, David M. Reif, Skylar W. Marvel

“…This is especially true when considering individual and population-level diversity, where the myriad combinations of real-world exposures magnify the combinatoric challenges. The GeoTox framework offers a tractable solution by integrating geospatial exposure data from source-to-outcome in a series of modular, interconnected steps. …”
Get full text

Preparation of future teachers for innovative activities in pedagogical and technological educational environment by N. I. Naumkin, N. N. Shekshaeva, V. F. Kupryashkin, E. V. Zabrodina

“…The environment includes conceptually-targeted, infrastructural, content-based, psychological-didactic, methodological-technological and relaxation-diagnostic components, its features are the following: 1) focus on innovative training of technology teachers as directly related to the material objects of the innovative economy of the country; 2) universality in the form of the possibility of using it to solve other educational tasks; 3) graphical visualisation of the environment model with an indication of the hierarchy and interrelation of components, its scale, combinatoricity and functional sufficiency; 4) compliance of the environment with all the requirements of regulatory documents on educational activities at the university; 5) possibility of full-scale implementation of modern approaches to learning (innovative, personalised, environmental, project, etc.); 6) possibility of constant monitoring and control of the implementation of the environment within its relaxation and diagnostic component; 7) use of modern educational technologies, including digital; 8) possibility of obtaining specialised knowledge and studying other disciplines within the framework of using network learning; 9) innovativeness of the environment, determined by the novelty of the approach to teaching the teachers innovation technology and its effectiveness.To teach innovation activity in this environment, a model of a methodological system for the formation of competence in innovation activity among future technology teachers has been created, combining conceptually-targeted, meaningful, instrumental-activity and reflexive-evaluative components. …”
Get full text