Related papers: On the conservation results for local reflection p…
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate…
Rice's theorem shows that nontrivial extensional properties of partial recursive functions are undecidable. For finite weighted Boolean optimization/CSP-style slices, a Rice-style structural analogue holds for tractability classification:…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
We establish several results concerning the expected general phenomenon that, given a multiplicative function $f:\mathbb{N}\to\mathbb{C}$, the values of $f(n)$ and $f(n+a)$ are "generally" independent unless $f$ is of a "special" form.…
We study local-global principles for torsors under reductive linear algebraic groups over semi-global fields; i.e., over one variable function fields over complete discretely valued fields. We provide conditions on the group and the…
In this paper we propose a general functorial definition of the operation of \emph{local tropicalization} in commutative algebra. Let $R$ be a commutative ring, $\Gamma$ a finitely generated subsemigroup of a lattice, $\gamma : \Gamma…
For some Maltsev conditions $\Sigma$ it is enough to check if a finite algebra $\mathbf A$ satisfies $\Sigma$ locally on subsets of bounded size, in order to decide, whether $\mathbf A$ satisfies $\Sigma$ (globally). This local-global…
Let $\psi_1,...,\psi_k$ be maps from Z to an additive abelian group with positive periods $n_1,...,n_k$ respectively. We show that the function $\psi=\psi_1+...+\psi_k$ is constant if $\psi(x)$ equals a constant for |S| consecutive integers…
This is the second in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars.…
This note recalls the representation of regular theories T in terms of set-valued functors on models given by Makkai(1990), and explicitly states the representation theorem for the classifying topos Set[T] in terms of filtered colimit…
We investigate the locality properties of $T \overline T$-deformed CFTs within perturbation theory. Up to third order in the deformation parameter, we find a Hamiltonian operator which solves the flow equation, reproduces the Zamolodchikov…
Various problems on integers lead to the class of congruence preserving functions on rings, i.e. functions verifying $a-b$ divides $f(a)-f(b)$ for all $a,b$. We characterized these classes of functions in terms of sums of rational…
Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…
Latschev's theorem provides sufficient conditions on a metric space $M$ and $\delta > 0$ for the homotopy type of $M$ to agree with that of the Vietoris-Rips complex $\mathcal{R}^{\delta}(N)$ of any nearby space $N$ in the Gromov-Hausdorff…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…
We present a theory of gravity based on Einstein's general relativity that is motivated by the paradoxes associated with time in relativistic rotating frames and certain exact solutions of Einstein's equations. We show that we can resolve…
The aim of this work is to extend and prove the Onsager conjecture for a class of conservation laws that possess generalized entropy. One of the main findings of this work is the "universality" of the Onsager exponent, $\alpha > 1/3$,…
Schaeffer's regularity theorem for scalar conservation laws can be loosely speaking formulated as follows. Assume that the flux is uniformly convex, then for a generic smooth initial datum the admissible solution is smooth outside a locally…
We show that the equations which describe irreversible evolution of a system can be derived from a variational principle. We suggest a Lagrangian, which depends on the properties of the normal and the so-called "mirror-image" system. The…
We consider the following question arising in the theory of differential inclusions: given an elliptic set $\Gamma$ and a Sobolev map $u$ whose gradient lies in the quasiconformal envelope of $\Gamma$ and touches $\Gamma$ on a set of…