Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data

In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian

October 16, 1954 Football Program, UOP vs. Colorado A and M

https://scholarlycommons.pacific.edu/ua-football/1145/thumbnail.jp

Morphological variations in cadmium sulfide nanocrystals without phase transformation

A very novel phenomenon of morphological variations of cadmium sulfide (CdS) nanorods under the transmission electron microscopy (TEM) beam was observed without structural phase transformation. Environmentally stable and highly crystalline CdS nanorods have been obtained via a chemical bath method. The energy of the TEM beam is believed to have a significant influence on CdS nanorods and may melt and transform them into smaller nanowires. Morphological variations without structural phase transformation are confirmed by recording selected area electron diffraction at various stages. The prepared CdS nanorods have been characterized by X-ray powder diffraction, TEM, UV-Vis spectroscopy, and photoluminescence spectroscopy. The importance of this phenomenon is vital for the potential application for CdS such as smart materials

Existence of solutions for a system of coupled nonlinear stationary bi-harmonic Schrodinger equations

We obtain existence and multiplicity results for the solutions of a class of coupled semilinear bi-harmonic Schrodinger equations. Actually, using the classical Mountain Pass Theorem and minimization techniques, we prove the existence of critical points of the associated functional constrained on the Nehari manifold. Furthermore, we show that using the so-called fibering method and the Lusternik-Schnirerman theory there exist infinitely many solutions, actually a countable family of critical points, for such a semilinear bi-harmonic Schrodinger system under study in this work.The authors like to thank the anonymous Referee by his valuable suggestions, helpful comments which further improved the content and presentation of the paper. The first and third authors have been partially supported by the Ministry of Economy and Competitiveness of Spain under research project MTM2012-33258. The second author has been partially supported by the Ministry of Economy and Competitiveness of Spain and FEDER funds under research project MTM2013-44123-P.Publicad

On some Critical Problems for the Fractional Laplacian Operator

We study the effect of lower order perturbations in the existence of positive solutions to the following critical elliptic problem involving the fractional Laplacian: (-\Delta)^{\alpha/2}u=\lambda u^q+u^{\frac{N+\alpha}{N-\alpha}}, \quad u>0 &\quad in \Omega, u=0&\quad on \partial\Omega,$$ where $\Omega\subset\mathbb{R}^N$ is a smooth bounded domain, $N\ge1$, $\lambda>0$, $0<q<\frac{N+\alpha}{N-\alpha}$, $0<\alpha<\min\{N,2\}$. For suitable conditions on $\alpha$ depending on $q$, we prove: In the case $q<1$, there exist at least two solutions for every $0<\lambda<\Lambda$ and some $\Lambda>0$, at least one if $\lambda=\Lambda$, no solution if $\lambda>\Lambda$. For $q=1$ we show existence of at least one solution for $01$ the existence is shown for every $\lambda>0$. Also we prove that the solutions are bounded and regular

Agricultural to Urban Water Transfers in Colorado: An Assessment of the Issues and Options

iii, 82 p. ; 28 cmhttps://scholar.law.colorado.edu/books_reports_studies/1063/thumbnail.jp

BRAIN ACTIVATION AND CONNECTIVITY IN NON-DISABLED MULTIPLE SCLEROSIS PATIENTS

Multiple sclerosis (MS) is the most common demyelinating disease affecting the central nervous system. There is no cure for MS and current therapies have limited efficacy. While the majority of individuals with MS develop significant clinical disability, a subset experiences a disease course with minimal impairment even in the presence of significant apparent tissue damage on magnetic resonance imaging (MRI). The current studies combined functional MRI and diffusion tensor imaging (DTI) to elucidate brain mechanisms associated with lack of clinical disability in patients with MS. Recent evidence has implicated cortical reorganization as a mechanism to limit the clinical manifestation of the disease. Functional MRI was used to test the hypothesis that non-disabled MS patients (Expanded Disability Status Scale ≤ 1.5) show increased recruitment of cognitive control regions (dorsolateral prefrontal and anterior cingulate cortex) while performing sensory, motor and cognitive tasks. Compared to matched healthy controls, patients increased activation of cognitive control brain regions when performing non-dominant hand movements and the 2-back working memory task. Using dynamic causal modeling, we tested whether increased cognitive control recruitment is associated with alterations in connectivity in the working memory functional network. Patients exhibited similar network connectivity to that of control subjects when performing working memory tasks. We subsequently investigated the integrity of major white matter tracts to assess structural connectivity and its relation to activation and functional integration of the cognitive control system. Patients showed substantial alterations in callosal, inferior and posterior white matter tracts and less pronounced involvement of the corticospinal tracts and superior longitudinal fasciculi (SLF). Decreased structural integrity within the right SLF in patients was associated with decreased performance, and decreased activation and connectivity of the cognitive control system when performing working memory tasks. These studies suggest that patient with MS without clinical disability increase cognitive control system recruitment across functional domains and rely on preserved functional and structural connectivity of brain regions associated with this network. Moreover, the current studies show the usefulness of combining brain activation data from functional MRI and structural connectivity data from DTI to improve our understanding of brain adaptation mechanisms to neurological disease