Related papers: Mechanics and special relativity: tutorial problem…
This thesis starts from a review on current research on the local hypoellipticity of the $\bar\partial$-Neumann problem. It presents the classical method of regularity from estimates of the energy: subelliptic as well as superlogarithmic.…
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…
The paper discusses the creation of a multimodal dataset of Russian-language scientific papers and testing of existing language models for the task of automatic text summarization. A feature of the dataset is its multimodal data, which…
Large language models (LLMs) have demonstrated remarkable capabilities in solving complex reasoning tasks, particularly in mathematics. However, the domain of physics reasoning presents unique challenges that have received significantly…
This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
Investigations related to expertise in problem solving and ability to transfer learning from one context to another are important for developing strategies to help students perform more expert-like tasks. Here we analyze written responses…
These examples are absent in the text of "Mechanics of liquids and gas, or mechanics of the inertless mass", as it was said in "Foreword of the editor" (Part I of this monograph). The editor places the missing text separately since some…
Doing mathematics implies three levels of manipulation: manipulating the abstract, manipulating symbols and manipulating logic. Teaching mathematics therefore involves the teacher proposing situations in which pupils can explore a small…
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a given problem into a representation that is easier to exploit for solving it. A major focus while helping introductory physics students learn problem…
We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic…
Analyzed models of learning, which take into account that: 1) the rate of increase of student's knowledge is proportional to the difference between levels of teacher's requirements and prior knowledge; 2) if the requirements are too high,…
These are the commentaries for a volume of reprints of my selected papers with commentaries that I am preparing for publication by World Scientific. Contents: Preface; (1)Early Years, and Condensed Matter Physics; (2) High Energy Neutrino…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
The second part of the monograph considers the application of the theory of ideal fluid to real fluids and gases. It contains eight examples of the practical application of the theory of inertial mass, a design diagram of a device for…
We give an abridged account of a continued string of studies in condensed matter physics and in complex systems that span five decades. We provide links to access abstracts and full texts of a selected list of publications. The studies were…
Background: Software modelling is a creative yet challenging task. Modellers often find themselves lost in the process, from understanding the modelling problem to solving it with proper modelling strategies and modelling tools. Students…
Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Problem solvers may generate diagrams to orient to a scenario, to organize information, to directly extract an answer, or as a tool of…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…