Related papers: A truncated second main theorem for algebraic tori…

We generalise various theorems for finding indiscernible trees and arrays to positive logic: based on an existing modelling theorem for s-trees, we prove modelling theorems for str-trees, str$_0$-trees (the reduct of str-trees that forgets…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

We classify up to conjugacy the subgroups of certain types in the full, in the affine, and in the special affine Cremona groups. We prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results in the…

We determine the complete spacetime action to first order in $\alpha'$ for the massless fields of bosonic string theory compactified on a $d$-dimensional torus. A fully systematic procedure is developed that brings the action into a minimal…

We consider a field $f \circ T_1^{i_1} \circ \cdots \circ T_d^{i_d}$ where $T_1, \dots , T_d$ arecommuting transformations, one of them at least being ergodic. Considering the case of commuting filtrations, we are interested by giving…

We present a fixed point theorem for a class of (potentially) non-monotonic functions over specially structured complete lattices. The theorem has as a special case the Knaster-Tarski fixed point theorem when restricted to the case of…

Let $m\geq 3$. Suppose that $$ 1-2^{-2^{m^24^m}}<\gamma<1. $$ Then the set $$ \{p\text{ prime}:\, p=[n^{\frac1\gamma}]\text{ for some }n\in{\mathbb N}\} $$ contains infinitely many non-trivial $m$-term arithmetic progressions.

We provide an extension of the Gromov--Zimmer Embedding Theorem for Cartan geometries of [3] to tractor bundles carrying any invariant connection, including tractor connections and prolongation connections of first BGG operators for…

The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be…

We introduce a general scheme to consistently truncate equations of motion for Green's functions. Our scheme is guaranteed to generate physical Green's functions with real excitation energies and positive spectral weights. There are free…

In this work we introduce a new algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that…

Employing the general ordering theorem, operational methods and the incomplete 2-dimensional Hermite polynomials we have derived the t-ordered expansion of the Fock space projectors. Using the result, a new integration formula regarding…

We prove a tropical analogue of Cartan's second main theorem for holomorphic curves intersecting hyperplanes in general position--a setting that was not fully resolved by previous tropical Nevanlinna theory. Two versions are obtained. The…

The Gy\'arf\'as tree packing conjecture states that any set of $n-1$ trees $T_{1},T_{2},..., T_{n-1}$ such that $T_i$ has $n-i+1$ vertices pack into $K_n$. We show that $t=1/10n^{1/4}$ trees $T_1,T_2,..., T_t$ such that $T_i$ has $n-i+1$…

The objective of this work is the construction of `Boyd-Wong fixed point theorem' in the setting of generalized parametric metric space and discussion its application on existence criteria of solutions to a second order initial value…

We study the restriction of the Fourier transform to quadratic surfaces in vector spaces over finite fields. In two dimensions, we obtain the sharp result by considering the sums of arbitrary two elements in the subset of quadratic surfaces…

We determine a Groebner basis for the secant ideal of the toric ideal associated to the second hypersimplex, with respect to any circular term order. The Groebner basis of the secant ideal requires polynomials of odd degree up to n. This…

We introduce and study the following relation between 2 linear functions f,g on a vector space of dimension d<=3: exp(tf+g)=exp(tf)exp(g) for every t an integer. If d=2 then f,g are simultaneously trigonalizable. If d=3 the same relation…

We provide a visual and intuitive introduction to effectively calculating in 2-groups along with explicit examples coming from non-abelian 1- and 2-form gauge theory. In particular, we utilize string diagrams, tools similar to tensor…

Let A = S/J be a standard artinian graded algebra over the polynomial ring S. A theorem of Macaulay dictates the possible growth of the Hilbert function of A from any degree to the next, and if this growth is the maximal possible then…