On Fermat Diophantine functional equations,little Picard theorem and beyond

Aequationes mathematicae - We discuss equivalence conditions for the non-existence of non-trivial meromorphic solutions to the Fermat Diophantine equation $$f^m(z)+g^n(z)=1$$ with integers $$m,n\ge...     

Evaluation of the performance of a soft X-ray charger for the bipolar charging of nanoparticles

The use of soft X-rays in a neutrahzer represents an alternative technique that could replace conventional radioactive sources.In this study,we evaluated the charging characteristics of a soft X-ray aerosol neutralize!".In addition,the results from the evaluation of the soft X-ray charger were compared with results obtained using a neutralizer incorporating an ²⁴¹Am radioactive source.The tandem differential mobility analyzer technique was used previously to determine the size-dependent positive,negative,and neutral charge fractions of a soft X-ray neutralizer.This technique was used to show that the neutral fractions obtained using the soft X-ray charger agreed well with the predictions of bipolar diffusion charging theory,and that the soft X-ray charger could be used as a neutralizer for a scanning mobility particle sizer system.     

Investigation of the Effect of Artificial Internal Defects on the Tensile Behavior of Laser Powder Bed Fusion 17–4 Stainless Steel Samples: Simultaneous Tensile Testing and X-Ray Computed Tomography

Experimental Mechanics - Insufficient data are available to fully understand the effects of metal additive manufacturing (AM) defects for widespread adoption of the emerging technology....     

Solid‐state 31P NMR investigation on the status of guanine nucleotides in paclitaxel‐stabilized microtubules

Microtubule dynamics is a target for many chemotherapeutic drugs. In order to understand the biochemical effects of paclitaxel on the GTPase activity of tubulin, the status of guanine nucleotides in microtubules was investigated by ³¹P cross‐polarization magic angle spinning (CPMAS) NMR. Microtubules were freshly prepared in vitro in the presence of paclitaxel and then lyophilized in sucrose buffer for solid‐state NMR experiments. A ³¹P CPMAS NMR spectrum with the SNR of 25 was successfully acquired from the lyophilized microtubule sample. The broadness of the ³¹P spectral lines in the spectrum indicates that the molecular environments around the guanine nucleotides inside tubulin may not be as crystalline as reported by many diffraction studies. Deconvolution of the spectrum into four spectral components was carried out in comparison with the ³¹P NMR spectra obtained from five control samples. The spectral analysis suggested that about 13% of the nucleotides were present as GTP and 37% as GDP in the β‐tubulin (E‐site) of the microtubules. It was found that most of the GDPs were present as GDP‐P_i complex in the microtubules, which seems to be one of the effects of paclitaxel binding. Copyright © 2015 John Wiley & Sons, Ltd.     

The Cauchy problem for a spin-liquid model in three space dimensions

In this paper, we study the Cauchy problem for magnetic fluid of spin-liquid type with Mermin-Ho relation in the three-dimensional space and prove global existence and uniqueness of solutions. The proof is based on the equivalence relation between smooth solutions of the spin-liquid model and the systems of Schrödinger equations with Abelian gauge field. The Sobolev spaces with fractional derivatives are also used in our estimates.