Rigid extensions of algebraic frames

An extension G ≤ H of lattice-ordered groups is said to be a rigid extension if for each ${h \in H}An extension G ≤ H of lattice-ordered groups is said to be a rigid extension if for each h ? H{h \in H} there exists a g ? G{g \in G} such that h ^⊥⊥ = g ^⊥⊥. In this paper, we will define rigid extensions and some other generalizations in the context of algebraic frames satisfying the FIP. One of the main results is a characterization of rigid extensions using d-elements of the frame. We also show that a rigid extension between two algebraic frames satisfying the FIP will induce a homeomorphism between their corresponding minimal prime spaces with respect to both the hull-kernel topology and the inverse topology. Moreover, basic open sets map to basic open sets.     

Raman spectroscopy in experimental oral carcinogenesis: investigation of abnormal changes in control tissues

Oral cancer is a major cause of mortality in South Asian men owing to rampant tobacco abuse. Cancers are also reported in non‐tobacco habitués, especially women, attributed to chronic irritations from irregular/sharp teeth, improper fillings, and poorly fit dentures. Conventional screening approaches are shown to be effective for high‐risk groups (tobacco/alcohol habitués). Raman spectroscopy (RS) is being extensively explored as an alternate/adjunct tool for diagnosis and management of oral cancers. In a previous Raman study on sequential oral carcinogenesis using hamster buccal pouch model, misclassifications between spectra from control and carcinogen [7,12‐dimethylbenz(a)anthracene (DMBA)]‐treated tissues were observed. Histopathology of some control tissues suggested pathological changes, attributable to repeated forceps‐induced irritations/trauma during animal handling. To explore these changes, in the present study, we recorded spectra from three different types of controls – vehicle control (n = 45), vehicle contralateral (n = 45), and DMBA contralateral (n = 70) – exposed to varying degree of forceps handling, along with DMBA‐treated pouches (n = 70) using a 14‐week carcinogenesis protocol. Spectra certified on the basis of histopathology and abnormal cell proliferation (cyclin D1 expression) were used to build models that were evaluated by independent test spectra from an exclusive set of DMBA‐treated and control animals. Many DMBA‐contralateral, vehicle‐control, and vehicle‐contralateral spectra were identified as higher pathologies, which subsequently corroborated with histopathology/cyclin D1 expression. Repeated forceps‐mediated injuries/irritations, during painting and animal handling, may elicit inflammatory responses, leading to neoplasm. The findings of the study suggest that RS could identify micro‐changes. Further, RS‐based in vivo imaging can serve as a promising label‐free tool for screening even in the non‐habitué population where conventional screening is shown to be not effective. Copyright © 2016 John Wiley & Sons, Ltd.