<p style='text-indent:20px;'>We provide a new and very simple criterion of positive topological entropy for tree maps. We prove that map <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula> has if only some iterate id="M2">\begin{document}$ f^k periodic orbit with three aligned points consecutive in time, is, triplet ...

<p style='text-indent:20px;'>In this paper, we investigate the pointwise time analyticity of three differential equations. They are biharmonic heat equation, equation with potentials and some nonlinear equations power nonlinearity order <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>. The include all nonnegative one...

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ P $\end{document}</tex-math></inline-formula> be a linear, second-order, elliptic operator with real coefficients defined on noncompact Riemannian manifold id="M3">\begin{document}$ M and satisfies id="M4">\begin{document}$ P1 = 0 in id="M5">\begin{document}$ $\end{documen...

We find probability error bounds for approximations of functions f in a separable reproducing kernel Hilbert space id="M2"> H with id="M3"> K on base id="M4"> X , firstly terms finite linear combinations type id="M5"> x i and ...

We prove that given a measure preserving system \begin{document}$ (X,\mathcal{B},\mu,T_1,\dots, T_d) $\end{document} with commuting, ergodic transformations id="M2">\begin{document}$ T_i such id="M3">\begin{document}$ T_iT_j^{-1} are for all id="M4">\begin{document}$ i \neq j $\end{document}</i...

The current investigation was carried out to develop polyphenol-enriched functional drinks from oil industry waste. Purposely, polyphenols were extracted the mustard and sesame oilseed cakes through ultrasound-aided extraction alongside conventional mode for comparison purposes. Among cake extracts, with methanol ultrasonic exhibited best results TPC, DPPH, FRAP, ABTS, β-carotene as <math xmlns...

&lt;p style='text-indent:20px;'&gt;This paper deals with the long time asymptotics of flow &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ X $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; solution to vector-valued ODE: id="M2"&gt;\begin{document}$ X'(t, x) = b(X(t, x)) for id="M3"&gt;\begin{document}$ t\in \mathbb{R} $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&g...

&lt;p style='text-indent:20px;'&gt;We consider a conservative ergodic measure-preserving transformation &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ T $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; of id="M2"&gt;\begin{document}$ \sigma $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-finite measure space id="M3"&gt;\begin{document}$ (X, {\mathcal B},\mu) with...

Background Previous cross-sectional studies reported that smoking lowers the incidence of knee osteoarthritis, however, some show no correlation between and osteoarthritis. Thus relationship two has not been clarified [1,2]. To address this issue, we designed a retrospective cohort study to investigate association using large-scale claim database from Korea. best our knowledge, is first on oste...