Formation and Structure of Fluorescent Silver Nanoclusters at Interfacial Binding Sites Facilitating Oligomerization of DNA Hairpins

Fluorescent, DNA‐stabilized silver nanoclusters (DNA‐AgNCs) are applied in a range of applications within nanoscience and nanotechnology. However, their diverse optical properties, mechanism of formation, and aspects of their composition remain unexplored, making the rational design of nanocluster probes challenging. Herein, a synthetic procedure is described for obtaining a high yield of emissive DNA‐AgNCs with a C‐loop hairpin DNA sequence, with subsequent purification by size‐exclusion chromatography (SEC). Through a combination of optical spectroscopy, gel electrophoresis, inductively coupled plasma mass spectrometry (ICP‐MS), and small‐angle X‐ray scattering (SAXS) in conjunction with the systematic study of various DNA sequences, the low‐resolution structure and mechanism of the formation of AgNCs were investigated. Data indicate that fluorescent DNA‐AgNCs self‐assemble by a head‐to‐head binding of two DNA hairpins, bridged by a silver nanocluster, resulting in the modelling of a dimeric structure harboring an Ag₁₂ cluster.     

Concentrations of rare earth elements in sediments,mussels and fish from a Danish marine environment,Lillebaelt

Results for the content of the rare earth elements (REE), La, Ce, Nd, Sm, Eu, Tb, Yb and Lu in sediments, mussels and fish are presented for an area polluted by REE. The REE are emitted with the process waste water stream from a fertilizer production plant. The method of analysis has been INAA. An attempt to combine the INAA with a simple destruction/preconcentration method is described.     

Shifted identical bands: A new phenomenon

The levels in ¹⁶²Gd were identified in spontaneous fission studies. Its transition energies are remarkably similar to those in ¹⁶⁰Gd. From that work, an analysis of yrast bands in even-even proton to neutron-rich Ba to Pb nuclei led to the discovery of a new phenomenon, shifted identical bands (SIB). SIBs are yrast bands in neighboring nuclei (a, b) with moments of inertia which are identical when shifted by a constant amount κ, so J _1a (1+κ)=J _1b , from 2⁺ to 8⁺ and higher to 16⁺. Out of over 700 comparisons, 55 SIBs were found from stable to the most neutron-rich Ce-W nuclei with $\left| {\bar k} \right|$ between 1.5% and 13%, where the spread in κ is less than ±1%, and only four identical bands ( $\bar k \cong 0$ ). As examples, we found for ¹⁵⁸Sm-¹⁶⁰Gd, $\bar k = \left( { - 3.2_{ - 0.2}^{ + 0.1} } \right)\%$ (where the ± is the total spread in κ from ?3.1 to ?3.4); ¹⁵⁶Nd-¹⁶⁰Gd, (?10.6 _?0.2 ^+0.4 )%; ¹⁵⁸Sm-¹⁶⁰Sm, (3.4 _?0.3 ^+0.5 )%. The J ₁ values were fitted to a variable moment of inertia model with parameters J ₀ and C whose values correlate with the SIB J ₁ values. The SIBs are not correlated either with deformation or with the N _p N _n product of the IBA model.     

The early exercise region for Bermudan options on two underlyings

This paper investigates the early exercise region for Bermudan options on two underlying assets. We present a set of analytical validation results for the early exercise region which can be used as a means of validating pricing techniques. When all strike prices are identical we show the existence of an intersection point such that for any asset price pair below this point early exercise is always optimal. We develop an approximation to this point in the two asset put case. When the strike prices are not all equal, we show that three separate cases exist for the early exercise region. For a Bermudan put on two assets we present these cases and show that there exists a critical point in which the boundaries of the two asset early exercise region bifurcate. Comparisons are drawn between the Bermudan results presented and the corresponding American option results.     

Computation of nonautonomous invariant and inertial manifolds

We derive a numerical scheme to compute invariant manifolds for time-variant discrete dynamical systems, i.e., nonautonomous difference equations. Our universally applicable method is based on a truncated Lyapunov–Perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using (nonsmooth) inexact Newton, and globally using continuation algorithms. Compared to other algorithms, our approach is quite flexible, since it captures time-dependent, nonsmooth, noninvertible or implicit equations and enables us to tackle the full hierarchy of strongly stable, stable and center-stable manifolds, as well as their unstable counterparts. Our results are illustrated using a test example and are applied to a population dynamical model and the Hénon map. Finally, we discuss a linearly implicit Euler–Bubnov–Galerkin discretization of a reaction diffusion equation in order to approximate its inertial manifold.     

Gamma Vibrational Bands and Chiral Doublet Bands in A≈100 Neutron-rich Nuclei

The level structures of neutron-rich ~(105)Mo,~(106)Mo,~(108)Mo and 110Ru nuclei in A≈100 region have been carefully investigated by coincidence measurements of the prompt γ-rays populated in the spontaneous fission of ~(252)Cf with the Gammasphere detector array.In 105Mo,one-phonon K =9/2 and two-phonon K=13/2 γ-vibrational bands have been identified.In ~(108)Mo,one-phonon γ-vibrational band is expanded and two-phonon γ-vibrational band has been identified.Two similar sets of bands in ~(106)Mo and ~(110)Ru are observed to high spins,which have been proposed as the soft chiral γ-vibrational bands.The characteristics for these γ-vibrational bands and chiral doublet bands have been discussed.     

Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Research on calculus: what do we know and where do we need to go?

In this introductory paper we take partial stock of the current state of field on calculus research, exemplifying both the promise of research advances as well as the limitations. We identify four trends in the calculus research literature, starting with identifying misconceptions to investigations of the processes by which students learn particular concepts, evolving into classroom studies, and, more recently research on teacher knowledge, beliefs, and practices. These trends are related to a model for the cycle of research and development aimed at improving learning and teaching. We then make use of these four trends and the model for the cycle of research and development to highlight the contributions of the papers in this issue. We conclude with some reflections on the gaps in literature and what new areas of calculus research are needed.