Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities

We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given

Synthesis of H_xLi_1-xLaTiO₄ from quantitative solid-state reactions at room temperature

The layered perovskite HLaTiO4 reacts stoichiometrically with LiOH·H2O at room temperature to give targeted compositions in the series HxLi1-xLaTiO4. Remarkably, the Li+ and H+ ions are quantitatively exchanged in the solid state and this allows stoichiometric control of ion exchange for the first time in this important series of compounds

Probabilistic prediction of cyanobacteria abundance in a Korean reservoir using a Bayesian Poisson model

There have been increasing reports of harmful algal blooms (HABs) worldwide. However, the factors that influence cyanobacteria dominance and HAB formation can be site‐specific and idiosyncratic, making prediction challenging. The drivers of cyanobacteria blooms in Lake Paldang, South Korea, the summer climate of which is strongly affected by the East Asian monsoon, may differ from those in well‐studied North American lakes. Using the observational data sampled during the growing season in 2007–2011, a Bayesian hurdle Poisson model was developed to predict cyanobacteria abundance in the lake. The model allowed cyanobacteria absence (zero count) and nonzero cyanobacteria counts to be modeled as functions of different environmental factors. The model predictions demonstrated that the principal factor that determines the success of cyanobacteria was temperature. Combined with high temperature, increased residence time indicated by low outflow rates appeared to increase the probability of cyanobacteria occurrence. A stable water column, represented by low suspended solids, and high temperature were the requirements for high abundance of cyanobacteria. Our model results had management implications; the model can be used to forecast cyanobacteria watch or alert levels probabilistically and develop mitigation strategies of cyanobacteria blooms. Key Points A Bayesian hurdle Poisson model predicted cyanobacteria abundance Temperature, flushing rate, and water column stability were key factors The model forecasted cyanobacteria watch and alert levels probabilisticallyPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106958/1/wrcr20820.pd

Engineered Peptides for Applications in Cancer-Targeted Drug Delivery and Tumor Detection

Cancer-targeting peptides as ligands for targeted delivery of anticancer drugs or drug carriers have the potential to significantly enhance the selectivity and the therapeutic benefit of current chemotherapeutic agents. Identification of tumor-specific biomarkers like integrins, aminopeptidase N, and epidermal growth factor receptor as well as the popularity of phage display techniques along with synthetic combinatorial methods used for peptide design and structure optimization have fueled the advancement and application of peptide ligands for targeted drug delivery and tumor detection in cancer treatment, detection and guided therapy. Although considerable preclinical data have shown remarkable success in the use of tumor targeting peptides, peptides generally suffer from poor pharmacokinetics, enzymatic instability, and weak receptor affinity, and they need further structural modification before successful translation to clinics is possible. The current review gives an overview of the different engineering strategies that have been developed for peptide structure optimization to confer selectivity and stability. We also provide an update on the methods used for peptide ligand identification, and peptide-receptor interactions. Additionally, some applications for the use of peptides in targeted delivery of chemotherapeutics and diagnostics over the past 5 years are summarized

Nonlinear Klein-Gordon-Maxwell systems with Neumann boundary conditions on a Riemannian manifold with boundary

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary conditions or for the singularly perturbed Klein Gordon Maxwell system with mixed Dirichlet Neumann homogeneous boundary conditions. We prove that stable critical points of the mean curvature of the boundary generates solutions when the perturbation parameter is sufficiently small.Comment: arXiv admin note: text overlap with arXiv:1410.884

Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials

We study the existence of stationnary positive solutions for a class of nonlinear Schroedinger equations with a nonnegative continuous potential V. Amongst other results, we prove that if V has a positive local minimum, and if the exponent of the nonlinearity satisfies N/(N-2)<p<(N+2)/(N-2), then for small epsilon the problem admits positive solutions which concentrate as epsilon goes to 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.Comment: 22 page

Experimental library screening demonstrates the successful application of computational protein design to large structural ensembles

The stability, activity, and solubility of a protein sequence are determined by a delicate balance of molecular interactions in a variety of conformational states. Even so, most computational protein design methods model sequences in the context of a single native conformation. Simulations that model the native state as an ensemble have been mostly neglected due to the lack of sufficiently powerful optimization algorithms for multistate design. Here, we have applied our multistate design algorithm to study the potential utility of various forms of input structural data for design. To facilitate a more thorough analysis, we developed new methods for the design and high-throughput stability determination of combinatorial mutation libraries based on protein design calculations. The application of these methods to the core design of a small model system produced many variants with improved thermodynamic stability and showed that multistate design methods can be readily applied to large structural ensembles. We found that exhaustive screening of our designed libraries helped to clarify several sources of simulation error that would have otherwise been difficult to ascertain. Interestingly, the lack of correlation between our simulated and experimentally measured stability values shows clearly that a design procedure need not reproduce experimental data exactly to achieve success. This surprising result suggests potentially fruitful directions for the improvement of computational protein design technology

Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

A Hermetic On-Cryostat Helium Source for Low Temperature Experiments

We describe a helium source cell for use in cryogenic experiments that is hermetically sealed $in$ $situ$ on the cold plate of a cryostat. The source cell is filled with helium gas at room temperature and subsequently sealed using a cold weld crimping tool before the cryostat is closed and cooled down. At low temperature the helium condenses and collects in a connected experimental volume, as monitored via the frequency response of a planar superconducting resonator device sensitive to small amounts of liquid helium. This on-cryostat helium source negates the use of a filling tube between the cryogenic volumes and room temperature, thereby preventing unwanted effects such as such as temperature instabilities that arise from the thermomechanical motion of helium within the system. This helium source can be used in experiments investigating the properties of quantum fluids or to better thermalize quantum devices.Comment: 5 pages, 3 figure