Related papers: The Full Pythagorean Theorem
The notion of frontals in Euclidean space is introduced and the normal and tangent maps to frontals are studied for both geometrical and dynamical aspects of frontals. Moreover we observe that parallels of the tangent map to a frontal curve…
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. We also prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
We establish some characterizations of elliptic hyperboloids (resp., ellipsoids) in the $(n+1)$-dimensional Euclidean space ${\Bbb E}^{n+1}$, using the $n$-dimensional area of the sections cut off by hyperplanes and the $(n+1)$-dimensional…
We establish some new theorems on pentagon and pentagram.
A generalization of the law of total covariance is presented and proved.
We give an elementary proof of the group law for elliptic curves using explicit formulas.
We prove some Bernstein theorems for entire space-like submanifolds in pseudo-Euclidean spaces and, as a corollary, we obtain a new proof of the Calabi-Pogorelov theorem on global solutions of Monge-Ampere equations.
We present an algebraic generalization of Euler's theorem for quadrilaterals. Starting from the parallelogram identity in an inner product space, we derive Apollonius' identity and obtain Euler's quadrilateral identity in a unified vector…
We design new tools to study variants of Total Dual Integrality. As an application, we obtain a geometric characterization of Total Dual Integrality for the case where the associated polyhedron is non-degenerate. We also give sufficient…
In this paper, we prove and disprove several generalizations of unbounded versions of the Fuglede-Putnam theorem.
In this work we consider the meaningfulness of the concept parallel worlds. To that extent we propose the model of the infinite-dimensionaly multievent space, generating everettics altervers in each point of Minkowski space time. Our…
We discuss historical attempts to formulate a physical hypothesis from which Turing's thesis may be derived, and also discuss some related attempts to establish the computability of mathematical models in physics. We show that these…
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
We introduce the concept of quotient in PN spaces and give some examples. We prove some theorems with regard to the completeness of a quotient.
We generalize Hagopian's theorem characterizing solenoids to higher dimensions by showing that any homogeneous continuum admitting a fiber bundle projection onto a torus with totally disconnected fibers admits a compatible abelian…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
We classify and describe totally geodesic and parallel hypersurfaces for the entire class of Siklos spacetimes. A large class of minimal hypersurfaces is also described.
We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an…
We show that there exist reduced polytopes in three-dimensional Euclidean space. This partially answers the question posed by Lassak on the existence of reduced polytopes in $d$-dimensional Euclidean space for $d\geq 3$. Moreover, we prove…