The recently established generalized Gell-Mann–Low theorem is applied in lowest perturbative order to bound–state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann–Low Theorem retains, while being fully relativistic, many of the desirable features of the quantum mechanical approaches to bound states. In particular, no abnormal or unphy...

Starting in 2005, general logical metatheorems have been developed that guarantee the extractability of uniform effective bounds from large classes of proofs of theorems that involve abstract metric structures X. In this paper we adapt this to the class of CAT(κ)-spaces X for κ > 0 and establish a new metatheorem that explains specific bound extractions that recently have been achieved in this ...

We present a short and self-contained proof of Jin’s theorem about the piecewise syndeticity of difference sets which is entirely elementary, in the sense that no use is made of nonstandard analysis, ergodic theory, measure theory, ultrafilters, or other advanced tools. An explicit bound to the number of shifts that are needed to cover a thick set is provided. Precisely, we prove the following:...

Let X = {Xij : 1 ≤ i, j ≤ n} be an n× n array of independent random variables where n ≥ 2. Let π be a uniform random permutation of {1,2, . . . , n}, independent of X, and let W =∑ni=1 Xiπ(i). Suppose X is standardized so that EW = 0,Var(W)= 1. We prove that the Kolmogorov distance between the distribution of W and the standard normal distribution is bounded by 451 ∑n i,j=1 E|Xij |3/n. Our appr...

By theorems of Ferguson and Lacey (d = 2) and Lacey and Terwilleger (d > 2), Nehari’s theorem is known to hold on the polydisc D for d > 1, i.e., if Hψ is a bounded Hankel form on H(D) with analytic symbol ψ, then there is a function φ in L∞(Td) such that ψ is the Riesz projection of φ. A method proposed in Helson’s last paper is used to show that the constant Cd in the estimate ‖φ‖∞ ≤ Cd‖Hψ‖ g...

A bstract We prove a positive volume theorem for asymptotically AdS spacetimes: the maximal slice has nonnegative vacuum-subtracted volume, and vanishes if only spacetime is identically pure AdS. Under Complexity=Volume proposal, this constitutes holographic complexity theorem. The result features number of parallels with energy theorem, including assumption an condition that excludes false vac...

This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and modern equivariant moving frame a framework dubbed involutive frames. As an attestation fruitfulness our framework, we obtain new, constructive intuitive proof Lie-Tresse theorem (Fundamental basis theorem) first general upper bound on minimal number generating differential invariants for Li...

In this paper we find the lower bound of second-order nonlinearity of Boolean function fλ(x) = Trn 1 (λx p) with p = 22r + 2r + 1, λ ∈ F2r and n = 5r. It is also demonstrated that the lower bound obtained in this paper is much better than the lower bound obtained by Iwata-Kurosawa [14], and Gangopadhyay et al. (Theorem 1, [12]).

The Pearcey process is a universal point in random matrix theory and depends on parameter [Formula: see text]. Let text] be the variable that counts number of points this fall interval In note, we establish following global rigidity upper bound: where arbitrary. We also obtain similar bound for maximum deviation points, central limit theorem individual fluctuations. proof short combines recent ...

We show a reduction method to construct a code for the Gray-Wyner (GW) network from a given code for the Wyner-Ahlswede-Körner (WAK) network. By combining this reduction with a converse bound on the GW network, we derive a converse bound on the WAK network. The derived bound gives an alternative proof of the strong converse theorem for the WAK network.