Related papers: A higher-dimensional version of F\'ary's theorem
We show that the Jacobian conjecture of the two dimensional case is true.
New estimates on the maximal function associated to the linear Schrodinger equation are established
In this article, we prove a decomposition theorem on differential polynomials of theta functions of high level.
We state and prove a quantum-generalization of MacMahon's celebrated Master Theorem, and relate it to a quantum-generalization of the boson-fermion correspondence of Physics.
In this article, we go on to discuss about a series of infinite dimensional extension of the theorems in [3], [5], [6]. We also prove a similar Geraghty type constructions for Fisher ([5]) in infinite dimension, using similar techniques as…
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
We extend Painlev\'e's determinateness theorem to the case of first order ordinary differential equations in the complex domain with known terms allowed be multivalued in the dependent variable as well; multivaluedness is supposed to be…
In this paper, we consider sums of generalized polygonal numbers with repeats, generalizing Fermat's polygonal number theorem which was proven by Cauchy. In particular, we obtain the minimal number of generalized $m$-gonal numbers required…
In this paper we first offer an alternative approach to extend the original Fueter's Theorem in Dunkl-Clifford analysis to a version of the higher order case. Then this result is used to prove a generlized version of Fueter's Theorem with…
We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof…
In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].
This note concerns exponential sheaves and the "universal" Fourier transform on them. Fourier invertibility and the subsequent Fourier miracle is demonstrated. Further, t-structures and realizations are constructed and shown to have…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
In every dimension $d \geq 2$, we give an explicit formula that expresses the values of any Schwartz function on $\mathbb{R}^d$ only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres…
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
For a two-component Fermi gas in the unitarity limit (ie, with infinite scattering length), there is a well-known virial theorem, first shown by J. E. Thomas et al, Phys. Rev. Lett. 95, 120402 (2005). A few people rederived this result, and…
We show that the so called Elko equation can be derived from a 5-dimensional Dirac equation. We argue that this result can be relevant for dark matter and cosmological scenarios. We generalize our procedure to higher dimensions.
We prove the following generalization of Severi's Theorem: Let $X$ be a fixed complex variety. Then there exist, up to birational equivalence, only finitely many complex varieties $Y$ of general type of dimension at most three which admit a…
In this article we prove a theorem that will generalize the concurrence theorems that are leading to the Franke's point, Kariya's point, and to other remarkable points from the triangle geometry.