In this manuscript, we will study \({\tilde{o}}\)-convergence in (partially) ordered vector spaces and a kind of convergence space V. A V is called semi-order (in short space), if there exist an W operator T from into W. way, say that with respect to \(\{W, T\}\). net \(\{x_\alpha \}\subseteq V\) said be \({\{W,T\}}\)-order convergent \(x\in write \(x_\alpha \xrightarrow {\{W, T\}}x\)), wheneve...

Abstract We provide an abstract characterization for the Cuntz semigroup of unital commutative AI-algebras, as well a semigroups form $\operatorname {\mathrm {Lsc}} (X,\overline {\mathbb {N}})$ some $T_1$ -space X . In our investigations, we also uncover new properties that all AI-algebras satisfies.

Despite the recent discovery of superconductivity in Nd$_{1-x}$Sr$_{x}$NiO$_2$ thin films, absence and antiferromagnetism their bulk materials remain a puzzle. Here we report $^{1}$H NMR measurements on powdered Nd$_{0.85}$Sr$_{0.15}$NiO$_2$ samples by taking advantage enriched proton concentration after hydrogen annealing. We find large full width at half maximum spectrum, which keeps increasi...

Our aim is the development and analysis of numerical schemes for approximately solving backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two levels, i.e., $u(T_1)$ $u(T_2)$, we simultaneously recover initial data $u(0)$ $u_t(0)$ hence solution $u(t)$ all $t > 0$. First, existence, uniqueness, Lipschitz stab...