Search for Rare Decays of the Observed Higgs Boson and Additional Higgs Bosons with the ATLAS Detector

Physics of Atomic Nuclei - Searches for rare decays of the Standard Model Higgs boson and additional Higgs bosons are performed by the ATLAS experiment at the LHC. They use the unprecedented amount...     

Characterization of intrinsic ultracontractivity for one dimensional Schrödinger operators

We consider a Schrödinger operator $L=?d^2/d{x}^2+V(x)$ on $\mathbb{R}$, where V is a real-valued measurable function, and give an explicit and simple characterization of intrinsic ultracontractivity (IU) of the Schrödinger semigroup generated by L for a wide class of potentials. By making use of it, we also give new examples of potentials for which the semigroups satisfy (IU) or non-(IU).     

Seeded Polymerization of an Amide-Functionalized Diketopyrrolopyrrole Dye in Aqueous Media

The self-assembly of an amide-functionalized dithienyldiketopyrrolopyrrole (DPP) dye in aqueous media was achieved through seed-initiated supramolecular polymerization. Temperature- and time-dependent studies showed that the spontaneous polymerization of the DPP derivative was temporally delayed upon cooling the monomer solution in a methanol/water mixture. Theoretical calculations revealed that an amide-functionalized DPP derivative adopts an energetically favorable folded conformation in the presence of water molecules due to hydration. This conformational change is most likely responsible for the trapping of monomers in the initial stage of the cooperative supramolecular polymerization in aqueous media. However, the monomeric species can selectively interact with externally added fragmented aggregates as seeds through concerted π-stacking and hydrogen-bonding interactions. Consequently, the time course of the supramolecular polymerization and the morphology of the aggregated state can be controlled, and one-dimensional fibers that exhibit a J-aggregate-like bathochromically shifted absorption band can be obtained.     

Multifold factorizations of cyclic groups into subsets

Let $(G,+)$ be an abelian group. A finite multiset A over G is said to give a λ-fold factorization of G if there exists a multiset B over G such that each element of G occurs λ times in the multiset $A+B:=\{a+b:a\in A,b\in B\}$. In this article, restricting G to a cyclic group, we will provide sufficient conditions on a given multiset A under which the exact value or an upper bound of the minimum multiplicity λ of a factorization of G can be given by introducing a concept of ‘lcm-closure’. Furthermore, a couple of properties on a given factor A will be shown when A has a prime or prime power order (cardinality). A relation to multifold factorizations of the set of integers will be also glanced at a general perspective.     

Temporal freedom in mathematical thought: A philosophical–empirical enquiry

This paper seeks to introduce and elaborate on the notion of ‘temporal freedom’ in the context of mathematical thinking.The intention is to merge a philosophical and empirical discussion on this topic, and findings will be presented from a qualitative study in which 29 high-school students were invited to explore the symmetry group of a square during clinical interviews. The data indicate how the interviewees – who were given the opportunity to freely explore an unseen mathematical system – repeatedly brought past and future together in a tangible present during their investigations. In doing so they were exceptionally successful in engaging with advanced abstract algebra, far beyond what might have been expected at the outset.By using empirical data to exemplify an otherwise highly philosophical discussion, I hope to draw explicit attention to the temporal aspect of the human mind in mathematical action which instructional methods frequently fail to recognise, value and utilise.     

Homo‐double helix formation of an optically active conjugated polymer bearing carboxy groups and amplification of the helicity upon complexation with achiral and chiral amines

An optically active, m‐terphenyl‐based π‐conjugated polymer bearing carboxy groups was synthesized by the copolymerization of the diethynyl monomer bearing a carboxy group with (S,S)‐2,5‐bis(2‐methylbutoxy)‐1,4‐dibromobenzene using Sonogashira reaction. The copolymer showed a weak circular dichroism (CD) in the main‐chain chromophore region due to a homo‐double helix formation with an excess helical handedness biased by the chiral alkoxy substituents through self‐association. However, upon complexation with achiral amines, such as piperidine, the CD intensity of the polymer significantly increased resulting in the formation of a greater excess one‐handed homo‐double helix via hydrogen‐bonded inclusion complexation with the achiral amines between each strand, leading to the amplification of the helicity. A preferred‐handed homo‐double helix was also induced in the polymer in the presence of nonracemic amines. The effect of the achiral and chiral amines on the homo‐double helix formation was investigated by comparing the CD spectra of the polymer to those of its model dimer. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 990–999