First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

The Forgotten Pyrazines: Exploring the Dakin–West Reaction

Pyrazines are an underreported class of N-heterocycles available from nitrogen-rich biomass presenting an interesting functional alternative for current aromatics. In this work, access to pyrazines obtained from amino acids by using the 90 year old Dakin–West reaction was explored. After a qualitative screening several functional proteinogenic amino acids proved good substrates for this reaction, which were successfully scaled to multigram scale synthesis of the corresponding intermediate α-acetamido ketones. Subsequently, the conditions towards pyrazine formation using δ-amino-levulinic acid were optimized, and these were employed to synthesize a relevant set of five functional dimethylpyrazines in high purity. These pyrazines can be considered a versatile toolbox of aromatic building blocks for a wide range of applications, such as in the synthesis of polymers or metal–organic frameworks.     

Low- and high-energy solutions of nonlinear elliptic oscillatory problems

In this Note, we study the existence of low- or high-energy solutions for a class of elliptic problems containing a nonlinear term that oscillates either near the origin or at infinity. We point out the competition effect between the oscillatory nonlinearity, a polynomial growth term, and the values of a real parameter. The proofs combine related variational methods.     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).     

A sharp eigenvalue theorem for fractional elliptic equations

The invisibility graph I(X) of a set X ? R ^d is a (possibly infinite) graph whose vertices are the points of X and two vertices are connected by an edge if and only if the straight-line segment connecting the two corresponding points is not fully contained in X. We consider the following three parameters of a set X: the clique number ω(I(X)), the chromatic number χ(I(X)) and the convexity number γ(X), which is the minimum number of convex subsets of X that cover X.We settle a conjecture of Matou?ek and Valtr claiming that for every planar set X, γ(X) can be bounded in terms of χ(I(X)). As a part of the proof we show that a disc with n one-point holes near its boundary has χ(I(X)) ≥ log log(n) but ω(I(X)) = 3.We also find sets X in R⁵ with χ(X) = 2, but γ(X) arbitrarily large.     

Zinc oxide nanostructured platform for electrochemical detection of heavy metals

ZnO nanoparticles (ZnO-NP) were prepared by a facile precipitation technique using di-isopropyl amine as precipitating agent. The morpho-structure and porosity of the as-prepared nano-powder were investigated by FT-IR analysis, X-ray diffraction (XRD), scanning electron microscopy (SEM), and BET analysis. By drop-casting, a composite film was deposited to obtain ZnO-NP-Nafion/GCE modified electrode. The modified electrode was investigated by cyclic voltammetry, electrochemical impedance spectroscopy, and square wave anodic stripping voltammetry (SWASV) for the detection of Pb²⁺, Cd²⁺, Cu²⁺, and Fe³⁺, and it was successfully applied for the detection of Pb²⁺ and Cu²⁺ in real water samples.