A minimization problem involving a fractional Hardy-Sobolev type inequality

In this work, we obtain an existence of nontrivial solutions to a minimization problem involving a fractional Hardy-Sobolev type inequality in the case of inner singularity. Precisely, for $\lambda>0$ we analyze the attainability of the optimal constant $$\mu_{\alpha, \lambda}(\Omega):=\inf\left\{ [u]^2_{s,\Omega}+\lambda\int_{\Omega}|u|^2 \, dx \colon u\in H^s(\Omega), \, \int_{\Omega} \frac{|u(x)|^{2_{s,\alpha}}}{|x|^{\alpha}} \, dx=1 \right\},$$ where $0<s<1, n>4s, 0<\alpha<2s$, $2_{s,\alpha}=\frac{2(n-\alpha)}{n-2s}$, and $\Omega \subset \mathbb{R}^n$ be a bounded domain such that $0\in \Omega$.Comment: 11 page

Homogenization and optimal design in nonlocal diffusion

Fil: Ritorto, Antonella. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

H−H-convergence result for nonlocal elliptic-type problems via Tartar's method

In this work we obtain a compactness result for the $H-$convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.Comment: In this revision we added a new section that shows the Gamma-convergence of the associated energy functional

A simple and reliable protocol for mouse serum proteome profiling studies by use of two-dimensional electrophoresis and MALDI TOF/TOF mass spectrometry

<p>Abstract</p> <p>Background</p> <p>Unravelling the serum proteome is the subject of intensified research. In this regard, two-dimensional electrophoresis coupled with MALDI MS analysis is still one of the most commonly used method. Despite some improvements, there is the need for better protocols to enable comprehensive identification of serum proteins.</p> <p>Here we report a combination of two proteomic strategies, zoom in acidic and neutral part of 2-D gels and an application of two optimised matrix preparations for MALDI-MS analyses to simplify serum proteome mapping.</p> <p>Results</p> <p>Mouse serum proteins were separated by 2-D electrophoresis at the pH ranges 3–10 and 4–7, respectively. Then in gel tryptic digests were analysed by MALDI-MS. Notably, sample-matrix preparations consisted of either a thin-layer α-ciano-4-hydroxycinnamic acid (CHCA) matrix deposition or a matrix-layer 2,5-dihydroxybenzoic acid (DHB). This enabled an identification of 90 proteins. The herein reported method enhanced identification of proteins by 32% when compared with previously published studies of mouse serum proteins, using the same approaches. Furthermore, experimental improvements of matrix preparations enabled automatic identification of mouse proteins, even when one of the two matrices failed.</p> <p>Conclusion</p> <p>We report a simple and reliable protocol for serum proteome analysis that combines an optimized resolution of 2-D gels spots and improved sample-matrix preparations for MALDI-MS analysis. The protocol allowed automated data acquisition for both CHCA and DHB and simplified the MS data acquisition therefore avoiding time-consuming procedures. The simplicity and reliability of the developed protocol may be applied universally.</p

Cancer proteomics of mouse serum and liver tissue samples to discover candidate biomarkers for hepatocellular carcinoma (HCC) in c-Myc transgenic mice

[no abstract

Informal music learning in UNCG Ukes

The primary purpose of this case study was to understand what motivated members of UNCG Ukes, a community ukulele group, to participate in and continue to be a part of the ukulele group. The secondary purpose was to understand how participants of UNCG Ukes learned to make music, specifically in relationship to informal music learning approaches. Participants in this study were members of UNCG Ukes, an intergenerational ukulele group that met on the campus of the University of North Carolina Greensboro during the Spring semester of 2015. Lucy Green's informal music learning components (2002; 2008) were used as the theoretical framework guiding the investigation. Using case study methodology, several forms of data were collected, including video-recorded observations, audio-recorded individual interviews, field notes, memos, analysis of lead sheets and music notation, and artifacts including photos and drawings of the space. Results based on observation and interview data indicated that participants were motivated to participate in UNCG Ukes because they enjoyed learning to sing, and play ukulele with others. The approach participants used to learn music within this context largely aligned with Green's informal music learning components. Whereas Green suggested that an aural-only approach was preferred in informal music learning (2002; 2008), participants of UNCG Ukes used a pragmatic “whatever works” approach to learning tunes, including using aural and visual methods, such as YouTube videos and lead sheets