Let R be a commutative ring. The cup-length of R is defined by the greatest number n such that there exist x1, . . . , xn ∈ R \ R with x1 · · · xn , 0. We denote the cup-length of R by cup(R). In particular, for a space X and a commutative ring A, the cup-length of X with the coefficient A, is defined by cup(H̃(X; A)). We denote it by cupA(X). It is well-known that cupA(X) is a lower bound for t...

‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...

This study presents a finger-triggered portable polydimethylsiloxane suction cup that enables equipment-free microfluidic pumping. The key feature of this method is that its operation only involves a “pressing-and-releasing” action for the cup placed at the outlet of a microfluidic device, which transports the fluid at the inlet toward the outlet through a microchannel. This method is simple, b...

Translational regulation plays an essential role in development and often involves factors that interact with sequences in the 3' untranslated region (UTR) of specific mRNAs. For example, Nanos protein at the posterior of the Drosophila embryo directs posterior development, and this localization requires selective translation of posteriorly localized nanos mRNA. Spatial regulation of nanos tran...

The cup from which I am drinking water now is yellow, and I know that it is. Why does my belief that the cup is yellow count as knowledge? Presumably, the answer must involve some reference to my current perceptual experience: I see the cup, and I see that it is yellow. What is it for me to see that the cup is yellow? The obvious answer would seem to be that it is for me to stand in a certain r...

Comprehensive gait analysis of patients with Crowe type II and III developmental dysplasia of the hip (DDH) after successful total hip arthroplasty (THA) is lacking in the literature. This study evaluated gait function in joint kinematics after unilateral and bilateral THA in patients with DDH. In addition, the effect of high cup position on gait function was investigated. A total of 16 unilate...

PURPOSE Wnt2b is normally expressed at the optic cup lip and is implicated in ciliary body induction. The lens has often been considered an organizer for the anterior eye, but recent studies demonstrate that the anterior cell fates are correctly specified in the absence of the lens. This study uses Wnt2b as a marker to reveal the mechanism behind the specification of the anterior domain of the ...

G laucoma is a disease characterised by apoptotic ganglion cell death related, at least in part, to intraocular pressure. Any examination for glaucoma must therefore include some comment upon the health of these cells. Unfortunately, it is difficult to examine the ganglion cell layer ophthalmoscopically and so ophthalmologists typically rely on an analysis of a more visible ocular structure—the...

The clinical significance of human papillomavirus (HPV) in neck node metastasis from cancer of unknown primary (CUP) is not well established. We aimed to address the relationship of HPV status between node metastasis and the primary tumor, and also the relevance of HPV status regarding radiographically detected cystic node metastasis in head and neck squamous cell carcinoma (HNSCC) and CUP. HPV...

BACKGROUND Patients with cancer of unknown primary (CUP) have metastatic malignant disease without an identifiable primary site; it is the fourth most common cause of cancer death. OBJECTIVES To explore patients' informal and professional carers' experiences of CUP to inform development of evidence-based, patient-centred care. METHODS Qualitative study involving development of multiple expl...