Related papers: On the $\Pi^1_2$ consequences of $\Pi^1_1$-$\maths…

We adopt a novel formalism for the low-energy analysis of the $\gamma p \to K^{+}\pi\Sigma$ photoproduction reaction to calculate the $\pi\Sigma$ invariant mass distributions in the $\Lambda(1405)$ resonance region. The approach adheres to…

Chiral-scale perturbation theory $\chi$PT$_\sigma$ has been proposed as an alternative to chiral $SU(3)_L\times SU(3)_R$ perturbation theory which explains the $\Delta I = 1/2$ rule for kaon decays. It is based on a low-energy expansion…

Let $\pi:(E,\nabla^{E}) \to (M,g)$ be an affine submersion with horizontal distribution, where $\nabla^{E}$ is a symmetric connection and $M$ is a Riemannian manifold. Let $\sigma$ be a section of $\pi$, namely, $\pi \circ \sigma = Id_{M}$.…

$\Pi_1^1$-ranks are a natural tool for studying coanalytic sets in descriptive set theory. In the book "Classical descriptive set theory", Kechris provided a technique to build $\Pi_1^1$-ranks using derivatives. In this note we will prove a…

In this paper we continue the study of the most important structures on C-systems, the structures that correspond, in the case of the syntactic C-systems, to the $(Pi,lambda,app,beta,eta)$-system of inference rules. One such structure was…

We investigate immediately differentiable $C_0$-semigroups $(e^{-tA})_{t \geq 0}$ satisfying $\sup_{0 < t <1} t^{1/\beta}\|Ae^{-tA}\| < \infty$ for some $0 < \beta \leq 1$. Such $C_0$-semigroups are referred to as the Crandall--Pazy class…

The infinite pigeonhole principle for $k$ colors ($\mathsf{RT}_k$) states, for every $k$-partition $A_0 \sqcup \dots \sqcup A_{k-1} = \mathbb{N}$, the existence of an infinite subset~$H \subseteq A_i$ for some~$i < k$. This seemingly…

The results of analyses obtained in Part I are examined from the viewpoint of chiral symmetry. The mass spectra of pi pi system are widely believed to be suppressed generally near the threshold, because of the derivative coupling property…

The $\eta \to \pi^+ \pi^- \pi^0 \gamma$ decay is discussed in the general context of Chiral Perturbation Theory (ChPT), assuming that the low--energy constants (counter--terms) are saturated by vector-meson resonances. The $\eta \to \pi^+…

Hemaspaandra et al. proved that, for $m > 0$ and $0 < i < k - 1$: if $\Sigma_i^p \BoldfaceDelta DIFF_m(\Sigma_k^p)$ is closed under complementation, then $DIFF_m(\Sigma_k^p) = coDIFF_m(\Sigma_k^p)$. This sharply asymmetric result fails to…

Given an uncountable cardinal $\kappa$, we consider the question of whether subsets of the power set of $\kappa$ that are usually constructed with the help of the Axiom of Choice are definable by $\Sigma_1$-formulas that only use the…

In this paper we study local and global well-posedness of the following Cauchy problem: $$ \bigg \{ \begin{array}{rl} i\partial_t\Psi+\frac{1}{2}\Delta_{x}\Psi = A_0\Psi +\alpha |\Psi|^{\gamma-1}\Psi, & (t,x)\in\R\times\R,\\…

We study the process $\gamma\gamma\to\pi^0\pi^0$ involving the principle mechanisms, the structure of its cross section and the role of individual isoscalar-tensor resonances in the saturation of its energy spectrum.

The decays $\eta'\to3\pi^{0}$ and $\pi^{0}\pi^{+}\pi^{-}$ were consider in isobar model approach. Branching ratio and Dalitz-plot shape of the decay $\eta'\to3\pi^{0}$ can be explain by $a0$- and $\sigma$-meson contributions. The $\sigma$…

Kechris and Martin showed that the Wadge rank of the $\omega$-th level of the decreasing difference hierarchy of coanalytic sets is $\omega_2$ under the axiom of determinacy. In this article, we give an alternative proof of the…

We give the amplitude for $\gamma\gamma \rightarrow \pi^+\pi^-\pi^0$ in leading order chiral perturbation theory. For the case of real photons we calculate the total and differential cross section. Furthermore, we give the dependence of the…

We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a…

For a nonempty compact subset $\sigma$ in the plane, the space $AC(\sigma)$ is the closure of the space of complex polynomials in two real variables under a particular variation norm. In the classical setting, $AC[0,1]$ contains several…

Misestimates of $\sigma_{P_o}$, the \emph{uncertainty} in $P_o$ from a 2-state Bayes equation used for binary classification, apparently arose from $\hat{\sigma}_{p_i}$, the uncertainty in underlying pdfs estimated from experimental $b$-bin…

The scalar contributions to the radiative decays of light vector mesons into a pair of neutral pseudoscalars, $V\to P^0P^0\gamma$, are studied within the framework of the Linear Sigma Model. This model has the advantage of incorporating not…