Related papers: Some extensions in the Adams spectral sequence and…
We present a new manifestation of G\"odel's second incompleteness theorem and discuss its foundational significance, in particular with respect to Hilbert's program. Specifically, we consider a proper extension of Peano arithmetic…
Consider a random planar point process whose law is invariant under planar isometries. We think of the process as a random distribution of point charges and consider the electric field generated by the charge distribution. In Part I of this…
The secondary zeta function $Z(s)=\sum_{n=1}^\infty\alpha_n^{-s}$, where $\rho_n=\frac12+i\alpha_n$ are the zeros of zeta with $\Im(\rho)>0$, extends to a meromorphic function on the hole complex plane. If we assume the Riemann hypothesis…
We consider the tree-level amplitude, describing all 3 channels of the binary (pi ,K)-reaction, as a meromorphic polynomially bounded function of 3 dependent complex variables. Relying systematically on the Mittag-Leffler theorem, we…
Weinberg's theorem for \pi-\pi scattering, including the Adler zero at threshold in the chiral limit, is analytically proved for microscopic quark models that preserve chiral symmetry. Implementing Ward-Takahashi identities, the isospin 0…
We study an axially symmetric solution of a vortex in the Abelian-Higgs model at critical coupling in detail. Here we propose a new idea for a perturbative expansion of a solution, where the winding number of a vortex is naturally extended…
Asymptotic expansions are presented for the moments of bound states in one-dimensional anharmonic potentials. The results are derived by using the SAFE method and include only the first non-zero wave-related correction to the familiar…
Let $a\in (0,1)$ and let $F_s(a)$ be the periodized zeta function that is defined as $F_s(a) = \sum n^{-s} \exp (2\pi i na)$ for $\Re s >1$, and extended to the complex plane via analytic continuation. Let $s_n = \sigma_n + it_n, \, t_n >0…
We investigate localization of noninteracting particles with spins higher than 1/2 in a two-dimensional random potential in presence of spin-orbit coupling. We consider an integer spin ($s=1$) and a half-integer spin ($s=3/2$) belonging to…
We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays and Hudson. Entering $2,000,000$ Riemann zeros, we prove that there exists $x$ in the interval $[exp(727.951858),…
We construct asymptotic expansions for the normalised incomplete gamma function $Q(a,z)=\Gamma(a,z)/\Gamma(a)$ that are valid in the transition regions, including the case $z\approx a$, and have simple polynomial coefficients. For Bessel…
An analytic extension of the Reissner-Nordstrom solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at $r=0$. The metric is still singular in the new…
We consider a variant on the Tetranacci sequence, where one adds the previous four terms, then divides the sum by two until the result is odd. We give an algorithm for constructing "initially division-poor" sequences, where over an initial…
High-resolution spectroscopic observations of the W UMa-type binary Epsilon CrA obtained as a time monitoring sequence on four full and four partial nights within two weeks have been used to derive orbital elements of the system and discuss…
The paper presents fundamental metrical theorems for a class of continued fraction-like expansions known as $\theta$-expansions. We first prove Khinchine's Weak Law of Large Numbers for the sum of digits, followed by the Diamond-Vaaler…
Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown--York mass, to study a fill-in problem of realizing…
Let $\{u_n\}_{n=1}^{\infty}$ be the Sylvester's sequence (sequence A000058 in the OEIS), and let $ a_1 < a_2 < \cdots $ be any other positive integer sequence satisfying $ \sum_{i=1}^\infty \frac{1}{a_i} = 1 $. In this paper, we solve a…
We make use of the chiral two-loop representation of the pi K scattering amplitude [J. Bijnens, P. Dhonte and P. Talavera, JHEP 0405 (2004) 036] to investigate the isospin odd scattering length at next-to-next-to-leading order in the SU(3)…
We compute an asymptotic expansion in $1/c$ of the limit in $n$ of the empirical spectral measure of the adjacency matrix of an Erd\H{o}s-R\'enyi random graph with $n$ vertices and parameter $c/n$. We present two different methods, one of…
We confirm the long-standing prediction that $c=e\approx 2.718$ is the threshold for the emergence of a non-vanishing absolutely continuous part (extended states) at zero in the limiting spectrum of the Erd\H{o}s-Renyi random graph with…