A concentration phenomenon for semilinear elliptic equations

For a domain \Omega\subset\dR^N we consider the equation -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in $\Omega$ and negative outside, and such that the sets $\{Q_n>0\}$ shrink to a point $x_0\in\Omega$ as $n\to\infty$. We show that if $u_n$ is a nontrivial solution corresponding to $Q_n$, then the sequence $(u_n)$ concentrates at $x_0$ with respect to the $H^1$ and certain $L^q$-norms. We also show that if the sets $\{Q_n>0\}$ shrink to two points and $u_n$ are ground state solutions, then they concentrate at one of these points

Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems

We determine a class of Carathéodory functions G for which the minimum formulated in the problem (1.1) below is achieved at a Schwarz symmetric function satisfying the constraint. Our hypotheses about G seem natural and, as our examples show, they are optimal from some points of vie

Global bifurcation for asymptotically linear Schr\"odinger equations

We prove global asymptotic bifurcation for a very general class of asymptotically linear Schr\"odinger equations \begin{equation}\label{1} \{{array}{lr} \D u + f(x,u)u = \lam u \quad \text{in} \ {\mathbb R}^N, u \in H^1({\mathbb R}^N)\setmimus\{0\}, \quad N \ge 1. {array}. \end{equation} The method is topological, based on recent developments of degree theory. We use the inversion $u\to v:= u/\Vert u\Vert_X^2$ in an appropriate Sobolev space $X=W^{2,p}({\mathbb R}^N)$, and we first obtain bifurcation from the line of trivial solutions for an auxiliary problem in the variables (\lambda,v) \in {\mathbb R} \x X. This problem has a lack of compactness and of regularity, requiring a truncation procedure. Going back to the original problem, we obtain global branches of positive/negative solutions 'bifurcating from infinity'. We believe that, for the values of $\lambda$ covered by our bifurcation approach, the existence result we obtain for positive solutions of \eqref{1} is the most general so fa

Mechanosensitive Self-Replication Driven by Self-Organization

Self-replicating molecules are likely to have played an important role in the origin of life, and a small number of fully synthetic self-replicators have already been described. Yet it remains an open question which factors most effectively bias the replication toward the far-from-equilibrium distributions characterizing even simple organisms. We report here two self-replicating peptide-derived macrocycles that emerge from a small dynamic combinatorial library and compete for a common feedstock. Replication is driven by nanostructure formation, resulting from the assembly of the peptides into fibers held together by β sheets. Which of the two replicators becomes dominant is influenced by whether the sample is shaken or stirred. These results establish that mechanical forces can act as a selection pressure in the competition between replicators and can determine the outcome of a covalent synthesis.

Herbivorous fish rise as a destructive fishing practice falls in an Indonesian marine national park

Securing ecosystem functions is challenging, yet common priority in conservation efforts. While marine parks aim to meet this challenge by regulating fishing through zoning plans, their effectiveness hinges on compliance levels and may respond to changes in fishing practices. Here we use a speciose assemblage of nominally herbivorous reef fish in Karimunjawa National Park (zoned since 1989) to investigate whether areas subject to a restrictive management regime sustained higher biomass over seven years compared to areas where moderate and permissive regulations apply. Using a trait‐based approach we characterize the functional space of the entire species pool and ask whether changes in biomass translate into changes in functional structure. We track changes in predator biomass, benthic community structure, and fishing practices that could influence herbivore trajectories. Overall herbivore biomass doubled in 2012 compared to 2006–2009 and remained high in 2013 across all management regimes. We found no evidence that this biomass build‐up resulted from predator depletion or increased food availability but suggest it emerged in response to a park‐wide cessation of fishing with large drive nets known as muroami. The biomass increase was accompanied by a modest increase in taxonomic richness and a slight decrease in community‐scale rarity that did not alter functional redundancy levels. Subtle changes in both functional specialization and identity of assemblages emerged as generalist species with low intrinsic vulnerability to fishing recovered sooner than more vulnerable specialists. While this implies a recovery of mechanisms responsible for the grazing of algal turfs and detritus, restoring other facets of herbivory (e.g., macroalgal consumption) may require more time. An increase in the cost‐benefit ratio per journey of muroami fishing facilitated a ban on muroami nets that met minimal resistance. Similar windows of opportunity may emerge elsewhere in which gear‐based regulations can supplement zoning plans, especially when compliance is low. This does not advocate for implementing such regulations once a fishery has become unprofitable. Rather, it underlines their importance for breaking the cycle of resource depletion and low compliance to zoning, thus alleviating the resulting threats to food security and ecosystem integrity

Synthesis of Pyridinium Amphiphiles Used for Transfection and Some Characteristics of Amphiphile/DNA Complex Formation

Pyridinium amphiphiles have found practical use for the delivery of DNA into cells. Starting from 4-methylpyridine, a general synthesis has been devised for the production of pyridinium amphiphiles which allows variation in both the hydrophobic part and in the headgroup area of the compounds. By means of differential scanning microcalorimetry, zeta potential, particle size measurements and cryo electron microscopy, some characteristics of the pyridinium amphiphile/ DNA complexes have been determined.

Monitoring of unbound protein in vesicle suspensions with off-null ellipsometry

In studies on the binding of proteins to small unilamellar phospholipid vesicles (SUV), the concentration of unbound protein usually remains unknown, because the vesicles cannot be separated from the bulk solution. In the present study, this limitation was overcome by addition of a supported planar phospholipid bilayer to the cuvette containing a vesicle suspension. Ellipsometric measurement of the protein adsorption velocities on this bilayer allowed determination of the concentrations of unbound protein. At high protein concentrations the adsorption is rapidly completed and the usual null-ellipsometry is too slow to obtain well-defined initial adsorption rates. Therefore, an off-null technique was developed, allowing measurement of the adsorbed protein mass at time intervals of 20 ms. Binding of prothrombin and coagulation factor Xa was measured in SUV suspensions prepared from a 20Va dioleoylphosphatidylserine (DOPS) and 80Vo dioleoylphosphatidylcholine (DOPC) phospho-lipid mixture. For prothrombin, a dissociation constant Kd:140+27 nM (mean*S.E.) and maximal surface concentration fL".: (8.9 + 0.8) ' 10- 3 mole of protein per mole of lipid, were obtained. For factor Xa, these values were K d: 49.6 + 6.3 nM and 1-u *:Q3.0 t 1.4) ' 10-3 mole of protein per mole of lipid. These binding parameters are similar to those obtained earlier for planar bilayers. Apparently, the binding of factor Xa and prothrombin is not dependent on surface curvature. r2

From Predicting Solar Activity to Forecasting Space Weather: Practical Examples of Research-to-Operations and Operations-to-Research

The successful transition of research to operations (R2O) and operations to research (O2R) requires, above all, interaction between the two communities. We explore the role that close interaction and ongoing communication played in the successful fielding of three separate developments: an observation platform, a numerical model, and a visualization and specification tool. Additionally, we will examine how these three pieces came together to revolutionize interplanetary coronal mass ejection (ICME) arrival forecasts. A discussion of the importance of education and training in ensuring a positive outcome from R2O activity follows. We describe efforts by the meteorological community to make research results more accessible to forecasters and the applicability of these efforts to the transfer of space-weather research.We end with a forecaster "wish list" for R2O transitions. Ongoing, two-way communication between the research and operations communities is the thread connecting it all.Comment: 18 pages, 3 figures, Solar Physics in pres