let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

The notion of (m,n)-ideals of semigroups was introduced by Lajos [13, 14]. Later (m,n) quasi-ideals and (m,n) bi-ideals and generalized (m,n) bi-ideals were studied in various algebraic structures. The notion of a rough set was originally proposed by Pawlak [16] as a formal tool for modeling and processing incomplete information in information systems. Some authors have studied the algebraic pr...

A = area of the rough wall Aj = jth equal subarea of the rough region, A=NA B = empirical constant for the mean velocity profile on a rough wall; Eq. (29) CA = A-weighting factor CF = overall skin friction coefficient, 1 L R L 0 cf dx1 c = speed of sound in free field cf = local skin friction coefficient, w= 1 2 0U 2 cf0 = local skin friction coefficient at a distance xle from the leading edge ...

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.

The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

—The amount of data that has to be analysed and processed to assist decision making has significantly increased in recent years. These datasets may contain potentially useful, but as yet undiscovered, information and knowledge. This high dimensionality of datasets leads to the phenomenon known as the curse of dimensionality. When faced with difficulties resulting from the high dimension of a sp...

Active sonar pulses suffer time-spreading, distortion, and de-correlation due to multipath propagation and reflections from rough boundaries. Correlation of the received distorted pulse with the transmitted pulse leads to degradation in pulse compression gain in comparison to the ideal case of a received pulse being simply a time-shifted, amplitude-scaled replica propagated along a single direc...

An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-