Related papers: A generalization of Routh's triangle theorem
It is generalized Weyl conformal curvature tensor in the case of a conformal mappings of a generalized Riemannian space in this paper. Moreover, it is found universal generalizations of it without any additional assumption. A method used in…
It is shown that the deformed conifold solution with three-form flux, found by Klebanov and Strassler, is supersymmetric, and that it admits a simple F-theory description in terms of a direct product of the deformed conifold and a torus.…
For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and…
Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic curves, i.e., a statement relating certain labeled…
We exhibit a remarkable connection between sixth equation of Painleve list and infinite families of explicitly uniformizable algebraic curves. Fuchsian equations, congruences for group transformations, differential calculus of functions and…
The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…
We find some extensions of the Kraft-Russell Generic Equivalence Theorem and using it we obtain a simple proof of a result of Dubouloz and Kishimoto.
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
We establish Gromov's celebrated reconstruction theorem in Lorentzian geometry. Alongside this result, we introduce and study a natural concept of isomorphy of normalized bounded Lorentzian metric measure spaces. We outline applications to…
In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.
Leighton's graph covering theorem says that two finite graphs with a common cover have a common finite cover. We present a new proof of this using groupoids, and use this as a model to prove two generalisations of the theorem. The first…
We study the Carnot theorem and the configuration of points and lines in connection with it. It is proven that certain significant points in the configuration lie on the same lines and same conics. The proof of an equivalent statement…
The generalized Markov equations are deeply connected with the generalized cluster algebras of Markov type. We construct a deformed Fock-Goncharov tropicalization for the generalized Markov equations and prove that their tropicalized tree…
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
We prove new theorems which are higher-dimensional generalizations of the classical theorems of Siegel on integral points on affine curves and of Picard on holomorphic maps from $\mathbb{C}$ to affine curves. These include results on…
We introduce a notion of probabilistic convexity and generalize some classical globalization theorems in Alexandrov geometry. A weighted Alexandrov's lemma is developed as a basic tool.
We observe that the classical Borsuk-Ulam theorem has an easy generalization to maps from an n-manifold M^n to R^n. We point out a geometric corollary.
We extend Turaev's theory of Euler structures and torsion invariants on 3-manifolds to the case of vector fields having generic behavior on the boundary. This allows to easily define gluings of Euler structures and to develop a completely…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
A very simple but useful almost sure convergence theorem of probability is given.