On a Stability of Logarithmic-Type Functional Equation in Schwartz Distributions

We prove the Hyers-Ulam stability of the logarithmic functional equation of Heuvers and Kannappan f(x+y)-g(xy)-h(1/x+1/y)=0,  x,y>0, in both classical and distributional senses. As a classical sense, the Hyers-Ulam stability of the inequality |f(x+y)-g(xy)-h(1/x+1/y)|≤ϵ,  x,y>0 will be proved, where f,g,h:ℝ+→ℂ. As a distributional analogue of the above inequality, the stability of inequality ∥u∘(x+y)-v∘(xy)-w∘(1/x+1/y)∥≤ϵ will be proved, where u,v,w∈'(ℝ+) and ∘ denotes the pullback of distributions

Silicon nanowire devices

Transport measurements were carried out on 15–35 nm diameter silicon nanowires grown using SiH4 chemical vapor deposition via Au or Zn particle-nucleated vapor-liquid-solid growth at 440°C. Both Al and Ti/Au contacts to the wires were investigated. The wires, as produced, were essentially intrinsic, although Au nucleated wires exhibited a slightly higher conductance. Thermal treatment of the fabricated devices resulted in better electrical contacts, as well as diffusion of dopant atoms into the nanowires, and increased the nanowire conductance by as much as 10^4. Three terminal devices indicate that the doping of the wires is p type

The Light and Period Variations of the Eclipsing Binary BX Draconis

New CCD photometric observations of BX Dra were obtained for 26 nights from 2009 April to 2010 June. The long-term photometric behaviors of the system are presented from detailed studies of the period and light variations, based on the historical data and our new observations. All available light curves display total eclipses at secondary minima and inverse O'Connell effects with Max I fainter than Max II, which are satisfactorily modeled by adding the slightly time-varying hot spot on the primary star. A total of 87 times of minimum light spanning over about 74 yrs, including our 22 timing measurements, were used for ephemeris computations. Detailed analysis of the O-C diagram showed that the orbital period has changed in combinations with an upward parabola and a sinusoidal variation. The continuous period increase with a rate of +5.65 \times 10^-7 d yr^-1 is consistent with that calculated from the Wilson-Devinney synthesis code. It can be interpreted as a mass transfer from the secondary to the primary star at a rate of 2.74 \times 10^-7 M\odot yr^-1, which is one of the largest rates for contact systems. The most likely explanation of the sinusoidal variation with a period of 30.2 yrs and a semi-amplitude of 0.0062 d is a light-traveltime effect due to the existence of a circumbinary object. We suggest that BX Dra is probably a triple system, consisting of a primary star with a spectral type of F0, its secondary component of spectral type F1-2, and an unseen circumbinary object with a minimum mass of M3 = 0.23 M\odot.Comment: 24 pages, including 5 figures and 9 tables, accepted for publication in PAS

Hepatitis C Virus and Hepatocarcinogenesis

Hepatitis C virus (HCV) is an RNA virus that is unable to integrate into the host genome. However, its proteins interact with various host proteins and induce host responses. The oncogenic process of HCV infection is slow and insidious and probably requires multiple steps of genetic and epigenetic alterations, the activation of cellular oncogenes, the inactivation of tumor suppressor genes, and dysregulation of multiple signal transduction pathways. Stellate cells may transdifferentiate into progenitor cells and possibly be linked to the development of hepatocellular carcinoma (HCC). Viral proteins also have been implicated in several cellular signal transduction pathways that affect cell survival, proliferation, migration and transformation. Current advances in gene expression profile and selective messenger RNA analysis have improved approach to the pathogenesis of HCC. The heterogeneity of genetic events observed in HCV-related HCCs has suggested that complex mechanisms underlie malignant transformation induced by HCV infection. Considering the complexity and heterogeneity of HCCs of both etiological and genetic aspects, further molecular classification is required and an understanding of these molecular complexities may provide the opportunity for effective chemoprevention and personalized therapy for HCV-related HCC patients in the future. In this review, we summarize the current knowledge of the mechanisms of hepatocarcinogenesis induced by HCV infection

Kinetic Electron Cooling in Magnetic Nozzles: Experiments and Modeling

As long-distance space travel requires propulsion systems with greater operational flexibility and lifetimes, there is a growing interest in electrodeless plasma thrusters that offer the opportunity of improved scalability, larger throttleability, running on different propellants, and limit device erosion. The majority of electrodeless designs rely on a magnetic nozzle (MN) for the acceleration of the plasma, which has the advantage of utilizing the expanding electrons to neutralize the ion beam without the additional installation of a cathode. The plasma expansion in the MN is nearly collisionless, and a fluid description of electrons requires a non-trivial closure relation. Kinetic electron effects, and in particular electron cooling, play a crucial role in various physical phenomena such as energy balance, ion acceleration, and particle detachment. Based on the experimental and theoretical studies conducted in recognition of this importance, the fundamental physics of the electron cooling mechanism revealed in MNs and magnetically expanding plasma are reviewed. Especially, recent approaches from the kinetic point of view are discussed, and our perspective on the future challenges of electron cooling and the relevant physical subject of MN is presented