Fourier Series of the Periodic Bernoulli and Euler Functions

We give some properties of the periodic Bernoulli functions and study the Fourier series of the periodic Euler functions which are derived periodic functions from the Euler polynomials. And we derive the relations between the periodic Bernoulli functions and those from Euler polynomials by using the Fourier series

Pemphigus Foliaceus Associated with Psoriasis during the Course of Narrow-Band UVB Therapy: A Simple Coincidence?

Although psoriasis and bullous diseases are considered to be completely different disease entities, the literature has reported a few cases of psoriasis associated with bullous diseases, most of which are bullous pemphigoid. In limited cases, pemphigus foliaceus has also been reported in association with psoriasis. In most of them, pemphigus lesions usually developed on an untreated patient with a chronic history of psoriasis. Herein, we report a case of 53-year-old male with a chronic history of psoriasis who first developed generalized erosive lesions after 26 cycles of narrow-band ultraviolet B (NBUVB) therapy. A diagnosis of pemphigus foliaceus was made based on skin biopsy and direct immunofluorescence assay. Pemphigus lesions were well controlled with combination therapy of oral steroid and azathioprine. This is the first case where pemphigus foliaceus co-occurred with psoriasis during NBUVB therapy

High-performance and scalable metal-chalcogenide semiconductors and devices via chalco-gel routes

We report a general strategy for obtaining high-quality, large-areametal-chalcogenide semiconductor films from precursors combining chelated metal salts with chalcoureas or chalcoamides. Using conventional organic solvents, such precursors enable the expeditious formation of chalco-gels,which are easily transformed into the corresponding highperformance metal-chalcogenide thin films with large, uniform areas. Diverse metal chalcogenides and their alloys (MQx: M = Zn, Cd, In, Sb, Pb; Q = S, Se, Te) are successfully synthesized at relatively low processing temperatures (<400°C). The versatility of this scalable route is demonstrated by the fabrication of large-area thin-film transistors (TFTs), optoelectronic devices, and integrated circuits on a 4-inch Si wafer and 2.5-inch borosilicate glass substrates in ambient air using CdS, CdSe, and In2Se3 active layers. The CdSe TFTs exhibit a maximum field-effect mobility greater than 300 cm2 V-1 s-1 with an on/off current ratio of >107 and good operational stability (threshold voltage shift < 0.5 V at a positive gate bias stress of 10 ks). In addition,metal chalcogenide-based phototransistors with a photodetectivity of >1013 Jones and seven-stage ring oscillators operating at a speed of ∼2.6 MHz (propagation delay of < 27 ns per stage) are demonstrated. © 2018 The Authors.1