The disjointly non-singular (DN-S) operators T∈L(E,Y) from a Banach lattice E to space Y are those which strictly singular in no closed subspace generated by disjoint sequence of non-zero vectors. When is order continuous with weak unit, can be represented as dense ideal some L1(μ) space, and we show that each T∈DN-S(E,Y) admits an extension T‾∈DN-S(L1(μ),PO), where PO certain derive both T T⁎⁎...

We show that the number of quivers in the mutation class of a quiver of Dynkin type Dn is given by ∑ d|n φ(n/d) ( 2d d ) /(2n) for n ≥ 5. To obtain this formula, we give a correspondence between the quivers in the mutation class and certain rooted trees. Introduction Quiver mutation is an important ingredient in the definition of cluster algebras [FZ1]. It is an operation on quivers, which indu...

Background: Diabetic neuropathy (DN) is the most common complication of diabetes mellitus causing increased morbidity and mortality. Although international guidelines did not include vitamins dietary supplements in any line management, these agents were prescribed by a significant number physicians either as preventive or treatment DN. This study aimed to develop validated questionnaire that ex...

Tanshinone ⅡA (TⅡA) is widely used for the treatment of a number human diseases, including diabetic nephropathy (DN) (1). The present study was performed to examine the role of the transforming growth factor β (TGFβ)/p65 pathway under TⅡA treatment in a glomerular mesangial cell model of DN. Firstly, it was identified that TⅡA inhibited the proliferation of HBZY‑1 cells, while simultaneously su...

The aim of this study was to examine postnatal islet and beta-cell expansion in healthy female control mice and its disturbances in diabetic GIPR(dn) transgenic mice, which exhibit an early reduction of beta-cell mass. Pancreata of female control and GIPR(dn) transgenic mice, aged 10, 45, 90 and 180 days were examined, using state-of-the-art quantitative-stereological methods. Total islet and b...

We give a new interpretation of the derangement numbers dn as the sum of the values of the largest fixed points of all non-derangements of length n− 1. We also show that the analogous sum for the smallest fixed points equals the number of permutations of length n with at least two fixed points. We provide analytic and bijective proofs of both results, as well as a new recurrence for the derange...

Diabetic nephropathy (DN) is the leading cause of end stage renal disease in the Western world. Microalbuminuria (MA) is the earliest and most commonly used clinical index of DN and is independently associated with cardiovascular risk in diabetic patients. Although MA remains an essential tool for risk stratification and monitoring disease progression in DN, a number of factors have called into...