Let $$r,h\in {\mathbb {N}}$$ with $$r\ge 7$$ and let $$F(x,y)\in {Z}}[x ,y]$$ be a binary form such that $$\begin{aligned} F(x , y) =(\alpha x + \beta y)^r -(\gamma \delta y)^r, \end{aligned}$$ where $$\alpha $$ $$\beta $$\gamma $$\delta are algebraic constants -\beta \gamma \ne 0$$ . We establish upper bounds for the number of primitive solutions to Thue inequality $$0<|F(x, y)| \le h$$ improv...

The main objective of this paper is to calculate the metric dimension and resolving-domination number zero-divisor graphs direct product finite fields. Let $F_1, \ldots, F_n(n \geqslant 2)$ be We consider graph $\Gamma(R)$ ring $R=F_1 \times \cdots F_n$ $(n determine $\beta(\Gamma(R))$ $\gamma_r(\Gamma(R))$ If order each field two, then we prove that $\beta(\Gamma(R)) \leqslant n-1$ $\gamma_r(\...

1 Simple Fermi theory of beta decay 2 Beta decay is one of the most easily found kinds of radioactivity. As we have seen, this result of the weak interaction leads to conversion of a neutron into a proton or vice versa, with the necessary charge change being made possible by the emission of a positive or negative beta particle (positron or electron). To ensure conservation of lepton number, eac...

The properties of cellulases from Helix pomatia have been studied by many workers, including Seilliere (1906), Karrer, Schubert & Wehrli (1925), Karrer & Schubert (1926, 1928) and de Stevens (1955). Cellulolytic enzymes have also been found in other invertebrates, such as Teredo (Greenfield, 1955) and Ctenolep8ima lineata (Lasker & Giese, 1956), and in a wide range ofmicro-organisms which inclu...

We investigated the effects of spatial-selective attention on oscillatory neuronal dynamics in a tactile delayed-match-to-sample task. Whole-head magnetoencephalography was recorded in healthy subjects while dot patterns were presented to their index fingers using Braille stimulators. The subjects' task was to report the reoccurrence of an initially presented sample pattern in a series of up to...

The $\beta$ decay of the neutron-rich $^{134}$In and $^{135}$In was investigated experimentally in order to provide new insights into nuclear structure tin isotopes with magic proton number $Z=50$ above $N=82$ shell. $\beta$-delayed $\gamma$-ray spectroscopy measurement performed at ISOLDE facility CERN, where indium were selectively laser-ionized on-line mass separated. Three $\beta$-decay bra...