We use nonstandard topology and the g-topology to characterize normal, almost-normal, regular, almost-regular, semiregular spaces. The cluster [resp. 0-cluster] set relation is used to characterize regular, almostregular [resp. strongly-regular] spaces. The Whyburn [resp. Dickman] filter bases are characterized and it is shown that the cluster [resp. f-cluster] set relation restricted to the do...

Let S be a finitely generated standard multigraded algebra over an Artinian local ring A; M a finitely generated multigraded S-module. This paper answers to the question when mixed multiplicities of M are positive and characterizes them in terms of lengths of A-modules. As an application, we get interesting results on mixed multiplicities of ideals, and recover some early results in [Te] and [TV].

At present, the filter theory of $BL$textit{-}algebras has been widelystudied, and some important results have been published (see for examplecite{4}, cite{5}, cite{xi}, cite{6}, cite{7}). In other works such ascite{BP}, cite{vii}, cite{xiii}, cite{xvi} a study of a filter theory inthe more general setting of residuated lattices is done, generalizing thatfor $BL$textit{-}algebras. Note that fil...

The Dedekind–Birkhoff theorem for finite-height modular lattices has previously been generalized to complete modular lattices, using the theory of regular coverings. In this paper, we investigate regular coverings in lattices of filters and lattices of ideals, and the regularization strategy–embedding the lattice into its lattice of filters or lattice of ideals, thereby possibly converting a co...

R-regular Mth band filters are an important class of digital filters and are used in constructing Mth-band wavelet filter banks, where the regularity is essential. But this kind of filter has larger stopband peak errors compared with a minimax filter of the same length. In this paper, peak errors in stopband of R-regular 4th-band filters are reduced by means of superimposing two filters with su...

In drug-safety study, the measurements of QT intervals require to have a level of precision to detect small druginduced prolongation (~ 5 msec). This paper discusses a modified approach of ∏-shaped FIR Filter to optimize the quality of signal and improve the stability of QT/QTc interval measurements.The proposed filter is designed to have a time-dependent frequency characteristic based on pre-d...

in this article we introduce the concept of $z^circ$-filter on a topological space $x$. we study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $c(x)$,  the ring of real-valued continuous functions on a completely regular hausdorff space $x$. it is observed that $x$ is a compact space if and only if every $z^circ$-filter ...

Let $(R,\mathfrak m)$ be a Noetherian local ring of prime characteristic p > 0, and t an integer such that $H_{\mathfrak m}^{j}(R)/0^{F}_{H^{j}_{\mathfrak m}(R)}$ has finite length for all j < t. The aim this paper is to show there exists uniform bound Frobenius test exponents ideals generated by filter regular sequences at most