this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

a heyting algebra is a distributive lattice with implication and a dual $bck$-algebra is an algebraic system having as models logical systems equipped with implication. the aim of this paper is to investigate the relation of heyting algebras between dual $bck$-algebras. we define notions of $i$-invariant and $m$-invariant on dual $bck$-semilattices and prove that a heyting semilattice is equiva...

objectives: the aim of this study was to identify the role of attentional process in postural control using choice reaction time task while changing the visual and proprioceptive cues under difficult balance task (standing on one-leg). methods: this cross-sectional study was conducted by participating 20 young people (22.75±2.29). each subject performed one-leg standing as balance task for each...

Abstract Non-conventional torrefaction under partially oxidative conditions is an emerging cost-effective thermochemical pre-treatment method to improve the quality of biomass for energy applications. The literature lacks data on combustion torrefied oxygen-deficient atmosphere with actual reactor (inevitable non-uniformities in thermal environment). In this work, a dual mode fixed-bed (torrefa...

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

We introduce the notions of T-dual Rickart and strongly T-dual Rickart modules. We provide several characterizations and investigate properties of each of these concepts. It is shown that every free (resp. finitely generated free) $R$-module is T-dual Rickart if and only if $overline{Z}^2(R)$ is a  direct summand of $R$ and End$(overline{Z}^2(R))$ is a semisimple (resp. regular) ring. It is sho...

under favorable soil conditions such as existence of easily destructible organic compounds, balanced heat and moisture, adequate ventilation and abundant nutrients, organic materials are mineralized. once mineralizing occurs, mineral elements like p, s, ca, mg, k and other cations are released. a related study was conducted to determine the effect of seven organic fertilizers (leaf mold (lm), r...

anaerobic treatment methods are more suitable for the treatment of concentrated wastewater streams, offer lower operating costs, the production of usable biogas product. the aim of this study was to investigate the performance of an anaerobic fluidized bed reactor (afbr)-aerobic moving bed bio reactor (mbbr) in series arrangement to treat currant wastewater.the bed materials of afbr were cylind...