Related papers: Moon in a puddle and the four-vertex theorem
We generalize Luna's fundamental lemma to smooth morphisms between stacks with good moduli spaces. We also give a precise condition for when it holds for non-smooth morphisms and versions for coherent sheaves and complexes. This generalizes…
An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…
Three principal concepts regarding lunar formation have been examined: the accretion hypothesis, the mega-impact theory, and the multi-impact model. The multi-impact model amalgamates the salient facets of the mega-impact theory and the…
The applicability of the linear theory of elasticity to the Moon has been studied. As a criterion was taken the smallness of the strain tensor. The elastic moduli are obtained from the data of the project "Apollo". The pressure was…
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
We discuss the proof of a certain integral theorem obtained by C. G. Cullen, originally stated on the class of the analytic intrinsic functions on the quaternions. It is shown that this integral theorem is true for a larger class of…
We prove Union-Closed sets conjecture.
We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.
In the manuscript [v4], we prove the uniqueness of a generalized quadrangle of order (4,16).
We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.
The author gave a proof of a generalization of the Aztec diamond theorem for a family of $4$-vertex regions on the square lattice with southwest-to-northeast diagonals drawn in (Electron. J. Combin., 2014) by using a bijection between…
We present an elementary combinatorial proof of the celebrated Friendship theorem. The proof involves looking at independent sets and constructing a bound on their size which forces a contradiction.
The classical theory of cold-trapped ice on the Moon and some modern theories are reviewed and compared with observational constraints. The "standard model" for lunar ice posits that ice has accumulated in polar cold traps after the spin…
In [J. Combin. Theory Ser. B 70 (1997), 2-44] we gave a simplified proof of the Four-Color Theorem. The proof is computer-assisted in the sense that for two lemmas in the article we did not give proofs, and instead asserted that we have…
We generalize [3, Lemma 2.2] and [4, Proposition 2.3] and deduce a positive result on Hilbert's fourteenth problem. Further, we give a relatively transparent and elementary proof of [3, Theorem 1.1].
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
Discrete analogs of extrema of curvature and generalizations of the four-vertex theorem to the case of polygons and polyhedra are suggested and developed. For smooth curves and polygonal lines in the plane, a formula relating the number of…
While planar graphs are flat from a topological viewpoint, we observe that they are not from a geometric one. We prove that every planar graph can be embedded into a surface consisting of spheres, glued together in a tree-like fashion. As a…
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…