38,447 research outputs found
Nonlinear Boundary Value Problems via Minimization on Orlicz-Sobolev Spaces
We develop arguments on convexity and minimization of energy functionals on
Orlicz-Sobolev spaces to investigate existence of solution to the equation
\displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in}
\Omega under Dirichlet boundary conditions, where
is a bounded smooth domain, is a
suitable continuous function and
satisfies the Carath\'eodory conditions, while is a measure.Comment: 14 page
Real space mapping of topological invariants using artificial neural networks
Topological invariants allow to characterize Hamiltonians, predicting the
existence of topologically protected in-gap modes. Those invariants can be
computed by tracing the evolution of the occupied wavefunctions under twisted
boundary conditions. However, those procedures do not allow to calculate a
topological invariant by evaluating the system locally, and thus require
information about the wavefunctions in the whole system. Here we show that
artificial neural networks can be trained to identify the topological order by
evaluating a local projection of the density matrix. We demonstrate this for
two different models, a 1-D topological superconductor and a 2-D quantum
anomalous Hall state, both with spatially modulated parameters. Our neural
network correctly identifies the different topological domains in real space,
predicting the location of in-gap states. By combining a neural network with a
calculation of the electronic states that uses the Kernel Polynomial Method, we
show that the local evaluation of the invariant can be carried out by
evaluating a local quantity, in particular for systems without translational
symmetry consisting of tens of thousands of atoms. Our results show that
supervised learning is an efficient methodology to characterize the local
topology of a system.Comment: 9 pages, 6 figure
Non-Linear Supersymmetric -Models and their Gauging in the Atiyah-Ward Space-Time
We present a supersymmetric non-linear \s-model built up in the
superspace of Atiyah-Ward space-time. A manifold of the K\"ahler type comes out
that is restricted by a particular decomposition of the K\"ahler potential. The
gauging of the \s-model isometries is also accomplished in superspace.Comment: 15 pages, Latex, no figure
Endometriosis: A Rare Cause of Large Bowel Obstruction.
Large bowel obstruction can result in significant morbidity and mortality, especially in cases of acute complete obstruction. There are many possible causes, the most common in adults being colorectal cancer. Endometriosis is a benign disease, and the most affected extragenital location is the bowel, especially the rectosigmoid junction. However, transmural involvement and acute occlusion are very rare events. We report an exceptional case of acute large bowel obstruction as the initial presentation of endometriosis. The differential diagnosis of colorectal carcinoma may be challenging, and this case emphasizes the need to consider intestinal endometriosis in females at a fertile age presenting with gastrointestinal symptoms and an intestinal mass causing complete large bowel obstruction.info:eu-repo/semantics/publishedVersio
- …