Let \(\theta \) be an irrational number and \(\varphi a real number. \(C > 2\) \(\varepsilon 0\). There are infinitely many positive integers n free of prime factors \(> (\log )^C\), such that \(\Vert \theta + \varphi \Vert < n^{-\left( \frac{1}{3} - \frac{2}{3C}\right) \varepsilon }\). Here y\Vert is the distance from y to \(\mathbb Z\).

In recent works, arbitrary structural sets in the non-commutative Clifford analysis context have been used to introduce non-trivial generalizations of harmonic algebra valued functions $\mathbb{R}^m$. Being defined as solutions elliptic (generally non-strongly elliptic) partial differential equations, $(\varphi,\psi)$-inframonogenic and $(\varphi,\psi)$-harmonic do not share good structure prop...

In this work we study the monodromy group of covers $\varphi \circ \psi$ curves \linebreak $\mathcal{Y}\xrightarrow {\quad {\psi}} \mathcal{X} \xrightarrow \varphi} \mathbb{P}^{1}$, where $\psi$ is a $q$-fold cyclic \'etale cover and $\varphi$ totally ramified $p$-fold cover, with $p$ $q$ different prime numbers odd. We show that Galois $\mathcal{G}$ closure $\mathcal{Z}$ form $ \mathcal{G} = \...

Abstract Let $$A_{\varphi }$$ A φ denote the matrix of rotation with angle $$\varphi $$ Euclidean plane, FLOOR function which rounds a real point to nearest lattice down on left and ROUND for rounding off vector node lattice. We prove under natural assumption \not = k\f...

We prove standard results of group cohomology – namely, existence a long exact sequence, classification torsors via the first group, Shapiro’s lemma, Hochschild-Serre spectral decomposition cochain complex in direct product case, and Jannsen’s result on recovery problem for theories such as continuous, analytic, bounded, pro-analytic cohomology. also these certain monoids, applications we have ...

The scalar field theory with potential $V(\ensuremath{\varphi})=\frac{1}{2}{m}^{2}{\ensuremath{\varphi}}^{2}\ensuremath{-}\frac{1}{4}g{\ensuremath{\varphi}}^{4}$ ($g&gt;0$) is ill defined as a Hermitian but in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric framework it well defined, and has positive real energy spectrum for the case of spacetime dimension $D=1$. While methods used literature ...

Abstract In this paper, we study Hankel operators on the doubling Fock spaces for all possible $1\leq p,q&lt;\infty $ 1 ≤ p , q &lt; ∞ . We characterize those symbols f which $H_{f}$ H</mml...