A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

Given \(1\le q \le 2\) and \(\alpha \in \mathbb {R}\), we study the properties of the solutions of the minimum problem

$$\begin{aligned} \lambda (\alpha ,q)=\min \left\{ \dfrac{\displaystyle \int _{-1}^{1}|u'|^{2}dx+\alpha \left| \int _{-1}^{1}|u|^{q-1}u\, dx\right| ^{\frac{2}{q}}}{\displaystyle \int _{-1}^{1}|u|^{2}dx}, u\in H_{0}^{1}(-1,1),\,u\not \equiv 0\right\} . \end{aligned}$$

In particular, depending on \(\alpha \) and q, we show that the minimizers have constant sign up to a critical value of \(\alpha =\alpha _{q}\), and when \(\alpha >\alpha _{q}\) the minimizers are odd.

     

On induced Ramsey numbers for k‐uniform hypergraphs

Let denote the complete k‐uniform k‐partite hypergraph with classes of size t and the complete k‐uniform hypergraph of order s. One can show that the Ramsey number for and satisfies when t = s^o(1) as s →∞. The main part of this paper gives an analogous result for induced Ramsey numbers: Let be an arbitrary k‐partite k‐uniform hypergraph with classes of size t and an arbitrary k‐graph of order s. We use the probabilistic method to show that the induced Ramsey number (i.e. the smallest n for which there exists a hypergraph such that any red/blue coloring of yields either an induced red copy of or an induced blue copy of ) satisfies . © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 5–20, 2016     

Palladium‐Catalyzed Intramolecular Carbene Insertion into C(sp3)−H Bonds

A palladium‐catalyzed carbene insertion into C(sp³)?H bonds leading to pyrrolidines was developed. The coupling reaction can be catalyzed by both Pd⁰ and Pd^II, is regioselective, and shows a broad functional group tolerance. This reaction is the first example of palladium‐catalyzed C(sp³)?C(sp³) bond assembly starting from diazocarbonyl compounds. DFT calculations revealed that this direct C(sp³)?H bond functionalization reaction involves an unprecedented concerted metalation–deprotonation step.     

Toxic and essential metals determination in commercial seafood: Paracentrotus lividus by ICP-MS

Toxic and essential metals content was determined by inductively coupled plasma mass spectrometry in commercial sea urchins samples from the Mediterranean Sea and Pacific Ocean. Results show that Chilean samples have the highest values of Cd, As, Ni, Cr and V; Spanish samples have the maximum Hg content while Sicilian samples have the lowest content of toxic metals. The toxic metal traces were compared with the limits of European Community (EC) No. 1881/2006 for bivalve molluscs. All samples exceed Pb and Cd limit levels; regarding Hg levels, only Sicilian and Sardinian samples have Hg content below the EC limits. The dietary intake of toxic and essential elements was evaluated for an adult. Furthermore, our study highlights a correlation between the toxic elements content and the marine environmental conditions of the places of origin even though only the generic FAO fishing area is specified.     

Medicinal plants with anti-inflammatory activities

Medicinal plants have been the main remedy to treat various ailments for a long time and nowadays, many drugs have been developed from traditional medicine. This paper reviews some medicinal plants and their main constituents which possess anti-inflammatory activities useful for curing joint inflammation, inflammatory skin disorders, cardiovascular inflammation and other inflammatory diseases. Here, we provide a brief overview of quick and easy reading on the role of medicinal plants and their main constituents in these inflammatory diseases. We hope that this overview will shed some light on the function of these natural anti-inflammatory compounds and attract the interest of investigators aiming at the design of novel therapeutic approaches for the treatment of various inflammatory conditions.     

New Solvable Variants of the Goldfish Many‐Body Problem

A technique to manufacture solvable variants of the “goldfish” many‐body problem is introduced, and several many‐body problems yielded by it are identified and discussed, including cases featuring multiperiodic or isochronous dynamics.     

Mycoestrogen determination in cow milk: Magnetic solid‐phase extraction followed by liquid chromatography and tandem mass spectrometry analysis

Recently, magnetic solid‐phase extraction has gained interest because it presents various operational advantages over classical solid‐phase extraction. Furthermore, magnetic nanoparticles are easy to prepare, and various materials can be used in their synthesis. In the literature, there are only few studies on the determination of mycoestrogens in milk, although their carryover in milk has occurred. In this work, we wanted to develop the first (to the best of our knowledge) magnetic solid‐phase extraction protocol for six mycoestrogens from milk, followed by liquid chromatography and tandem mass spectrometry analysis. Magnetic graphitized carbon black was chosen as the adsorbent, as this carbonaceous material, which is very different from the most diffuse graphene and carbon nanotubes, had already shown selectivity towards estrogenic compounds in milk. The graphitized carbon black was decorated with Fe₃O₄, which was confirmed by the characterization analyses. A milk deproteinization step was avoided, using only a suitable dilution in phosphate buffer as sample pretreatment. The overall process efficiency ranged between 52 and 102%, whereas the matrix effect considered as signal suppression was below 33% for all the analytes even at the lowest spiking level. The obtained method limits of quantification were below those of other published methods that employ classical solid‐phase extraction protocols.     

More,or less,trivial matrix functional equations

Various functional equations satisfied by one or two (N × N)-matrices \({\mathbf{F}(z) }\) and \({\mathbf{G}(z) }\) depending on the scalar variable z are investigated, with N an arbitrary positive integer. Some of these functional equations are generalizations to the matrix case (N > 1) of well-known functional equations valid in the scalar (N = 1) case, such as \({\mathbf{F}(x) \, \mathbf{F}(y) = \, \mathbf{F}(x y) \, \rm and \, \mathbf{G}({\it x}) \, \mathbf{G}({\it y}) = \mathbf{G}({\it x+y}) }\); others—such as \({\mathbf{G}(y) \, \mathbf{F}(x) = \mathbf{F}(x) \, \mathbf{G}(xy) }\)—possess nontrivial solutions only in the matrix case (N > 1), namely their scalar (N = 1) counterparts only feature quite trivial solutions. It is also pointed out that if two (N × N)-matrices \({\mathbf{F}(x) \, \rm and \, \mathbf{G}({\it y})}\) satisfy the triplet of functional equations written above—and nontrivial examples of such matrices are exhibited— then they also satisfy an endless hierarchy of matrix functional relations involving an increasing number of scalar independent variables, the first items of which read \({\mathbf{F}(x_{1}) \, \mathbf{G}(y_{1}) \, \mathbf{F} (x_{2}) = \mathbf{F}(x_{1} x_{2}) \, \mathbf{G } (x_{2} y_{1}) \, \rm and \, \mathbf{G}({\it y}_{1}) \, \mathbf{F} ({\it x}_{1}) \, \mathbf{G} ({\it y}_{2}) = \mathbf{F} ({\it x}_{1}) \, \mathbf{G} ({\it x}_{1} {\it y}_{1}+{\it y}_{2}) }\).     

Globally generated vector bundles on the Segre threefold with Picard number two

We classify globally generated vector bundles on with small first Chern class, i.e. , . Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne–Serre correspondence.     

On topological filtrations of groups

The (weak) geometric simple connectivity and the quasi-simple filtration are topological notions of manifolds, which may be defined for discrete groups too. It turns out that they are equivalent for finitely presented groups, but the main problem is the absence of examples of groups which do not satisfy them. In this note we study some algebraic classes of groups with respect to these properties.