Related papers: A quantitative Balian-Low theorem for higher dimen…

A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.

We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…

In this paper we will be considering a basic geometric problem, the extension problem of classical Hamilton-Cartan variational theory to higher jet prolongations on fibered manifolds.

We construct extended Weil representations of unitary groups over finite fields geometrically, and show that they are Shintani lifts for Weil representations.

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We prove Carleson embeddings for Bergman-Orlicz spaces of the unit ball that extend the lower triangle estimates for the usual Bergman spaces.

An extension of Quantum Group is described. We propose to unite the quantum groups with parameter q and with parameter modularly dual to q.

We prove an x-ray estimate in general dimension which is stronger than the Kakeya estimates of Wolff. This generalizes an x-ray estimate in three dimensions which is also due to Wolff.

The factorization form of the integrands in the Cachazo-He-Yuan (CHY) formalism makes the generalized Kawai-Lewellen-Tye (KLT) relations manifest, thus amplitudes of one theory can be expanded in terms of the amplitudes of another theory.…

Poonen and Slavov recently developed a novel approach to Bertini irreducibility theorems over an arbitrary field, based on random hyperplane slicing. In this paper, we extend their work by proving an analogous bound for the dimension of the…

An technically interesting proof of a known theorem.

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 extend the classical Landesman-Lazer results to the setting of second order Hamilton-Jacobi-Bellman equations. A number of new phenomena appear.

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to…

Stretching the parameters of a Littlewood-Richardson coefficient of value 2 by a factor of n results in a coefficient of value n+1. We give a geometric proof of a generalization for representations of quivers.

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

We extend the results of Jones, Rosenblatt, and Wierdl concerning higher-dimensional oscillation in ergodic theory in a variety of ways. We do so by transference to the integer lattice, where we employ technique from (discrete) harmonic…

We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized…

This is an extension of the paper [14] by the author for the 2+1 dimensional Maxwell-Klein-Gordon equations in temporal gauge to the n+1 dimensional situation for $n \ge 3$. They are shown to be locally well-posed for low regularity data,…