Related papers: Memories with Solomon Marcus
We briefly describe each of the four topics: Schubert Calculus, Schubert Cell, Schubert Cycle, and Schubert Polynomials.
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logical system, e.g, boolean and heyting algebras, MV-algebras,…
We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…
This paper presents a brief account of some of the my early research interests. This historical account starts from my laurea thesis on Signal Theory and my master thesis on Computation Theory. It recalls some results in Combinatory Logic…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
This paper describes a series of activities in which students investigate and use the Ptolemaic, Copernican, and Tychonic models of planetary motion. The activities guide students through using open source software to discover important…
This paper is a faithful description of the author's career as a scientist, which often intersected that of Yves Couder. The emphasis of this paper is a true description of how the science that the author has been associated with really…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
This paper presents a comprehensive survey of various established mathematical models pertaining to Somitogenesis, a biological process. The study begins by revisiting and replicating the findings from prominent research papers in this…
In this small note I try to summarize some observations about Euclid's remarkable role in mathematics and about the ambient philosophy.
The unique and beautiful character of certain mathematical results and proofs is often considered one of the most gratifying aspects of engaging with mathematics. We study whether this perception of mathematical arguments having an…
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
We discuss the multiple summability of a multilinear map $T:X_1\times\cdots\times X_m\to Y$ when we have informations on the summability of the maps it induces on each coordinate. Our methods have applications to inclusion theorems for…
The application of mathematics and statistical methods to scholarly communication: scientometrics, has facilitated the systematic analysis of the modern digital tide of literature. This chapter reviews three of such applications:…
The interactive textbook is created for English-speaking students whose study on Mathematical Calculus is based on modern programs of Ukrainian higher educational institutions. It includes personal tasks and samples on ``Integral Calculus…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
The purpose of this project is to outline various philosophies on the metaphysics of mathematics that have been prominent since the time of Cantor, highlighting some biographical aspects that have influenced these ideas as well. The main…
Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
As a former engineering student, I have a great interest in a real world application of mathematics. Probability is something I can relate to. I am lucky enough that after I switched to Mathematics, this is one of many interests of my Ph.D.…