A new semifield of order 2

In [G. Lunardon, Semifields and linear sets of PG(1,q^t), Quad. Mat., Dept. Math., Seconda Univ. Napoli, Caserta (in press)], G. Lunardon has exhibited a construction method yielding a theoretical family of semifields of order q²ⁿ,n>1 and n odd, with left nucleus F_qⁿ, middle and right nuclei both F_q² and center F_q. When n=3 this method gives an alternative construction of a family of semifields described in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti, On a generalization of cyclic semifields, J. Algebraic Combin. 26 (2009), 1-34], which generalizes the family of cyclic semifields obtained by Jha and Johnson in [V. Jha, N.L. Johnson, Translation planes of large dimension admitting non-solvable groups, J. Geom. 45 (1992), 87-104]. For n>3, no example of a semifield belonging to this family is known.In this paper we first prove that, when n>3, any semifield belonging to the family introduced in the second work cited above is not isotopic to any semifield of the family constructed in the former. Then we construct, with the aid of a computer, a semifield of order 2¹⁰ belonging to the family introduced by Lunardon, which turns out to be non-isotopic to any other known semifield.     

A One-Pot Entry to a Novel 3-H-benzo[d]pyrazolo[1,5-b]isothiazole Ring System

Summary The phosphorus ylide obtained from the reaction between 2-aminobenzo[d]isothiazol-3-one and dimethyl acetylenedicarboxylate in the presence of triphenylphosphine undergoes a smooth intramolecular Wittig-type reaction to produce, in a one-pot reaction, 3-H-benzo[d]pyrazolo[1,5-b]isothiazole-2,3a-dicarboxylic acid dimethyl ester, a novel functionalized heterocyclic compound.     

New degree bounds for polynomial threshold functions

A real multivariate polynomial p(x ₁, …, x _n ) is said to sign-represent a Boolean function f: {0,1} ⁿ →{−1,1} if the sign of p(x) equals f(x) for all inputs x∈{0,1} ⁿ . We give new upper and lower bounds on the degree of polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs.     

Layered solutions with multiple asymptotes for non autonomous Allen–Cahn equations in {\mathbb {R}^{3}}

We consider a class of semilinear elliptic equations of the form $$ \label{eq:abs}-\Delta u(x,y,z)+a(x)W'(u(x,y,z))=0,\quad (x,y,z)\in\mathbb {R}^{3},$$ where ${a:\mathbb {R} \to \mathbb {R}}$ is a periodic, positive, even function and, in the simplest case, ${W : \mathbb {R} \to \mathbb {R}}$ is a double well even potential. Under non degeneracy conditions on the set of minimal solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W^{\prime}(q(x))=0,\ x\in\mathbb {R},\quad q(x)\to\pm1\,{\rm as}\, x\to \pm\infty,$$ we show, via variational methods the existence of infinitely many geometrically distinct solutions u of (0.1) verifying u(x, y, z) → ± 1 as x → ± ∞ uniformly with respect to ${(y, z) \in \mathbb {R}^{2}}$ and such that ${\partial_{y}u \not \equiv0, \partial_{z}u \not\equiv 0}$ in ${\mathbb {R}^{3}}$ .     

The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

Subcellular Duplex DNA and G‐Quadruplex Interaction Profiling of a Hexagonal PtII Metallacycle

Metal‐driven self‐assembly afforded a multitude of fascinating supramolecular coordination complexes (SCCs) with applications as catalysts, host–guest, and stimuli‐responsive systems. However, the interest in the biological applications of SCCs is only starting to emerge and thorough characterization of their behavior in biological milieus is still lacking. Herein, we report on the synthesis and detailed in‐cell tracking of a Pt₂L₂ metallacycle. We show that our hexagonal supramolecule accumulates in cancer cell nuclei, exerting a distinctive blue fluorescence staining of chromatin resistant to UV photobleaching selectively in nucleolar G4‐rich regions. SCC co‐localizes with epitopes of the quadruplex‐specific antibody BG4 and replaces other well‐known G4 stabilizers. Moreover, the photophysical changes accompanying the metallacycle binding to G4s in solution (fluorescence quenching, absorption enhancement) also take place intracellularly, allowing its subcellular interaction tracking.     

Optimizing the Size of Platinum Nanoparticles for Enhanced Mass Activity in the Electrochemical Oxygen Reduction Reaction

High oxygen reduction (ORR) activity has been for many years considered as the key to many energy applications. Herein, by combining theory and experiment we prepare Pt nanoparticles with optimal size for the efficient ORR in proton‐exchange‐membrane fuel cells. Optimal nanoparticle sizes are predicted near 1, 2, and 3 nm by computational screening. To corroborate our computational results, we have addressed the challenge of approximately 1 nm sized Pt nanoparticle synthesis with a metal–organic framework (MOF) template approach. The electrocatalyst was characterized by HR‐TEM, XPS, and its ORR activity was measured using a rotating disk electrode setup. The observed mass activities (0.87±0.14 A mg_Pt^?1) are close to the computational prediction (0.99 A mg_Pt^?1). We report the highest to date mass activity among pure Pt catalysts for the ORR within similar size range. The specific and mass activities are twice as high as the Tanaka commercial Pt/C catalysis.     

Shape reconstruction of metallic objects from intensity scattered field data only

We address an inverse scattering problem using only amplitude information of the scattered field. In particular, we are concerned with the reconstruction of the shape of a metallic planar obstacle, located in a known plane (aperture plane), starting from the knowledge of the intensity of the scattered field over two measurement planes in near zone and parallel to the aperture plane, when a single-frequency incident plane wave is exploited. The formulation of the inverse scattering problem is given under the physical optics approximation, and thus the resulting phase retrieval problem is quadratic. This allows us to apply some phase retrieval techniques already developed for antenna diagnostics. Reconstruction results with synthetic data indicate the feasibility of the proposed approach.