Strategies for the Controlled Covalent Double Functionalization of Graphene Oxide

Graphene oxide (GO) is a versatile platform with unique properties that have found broad applications in the biomedical field. Double functionalization is a key aspect in the design of multifunctional GO with combined imaging, targeting, and therapeutic properties. Compared to noncovalent functionalization, covalent strategies lead to GO conjugates with a higher stability in biological fluids. However, only a few double covalent functionalization approaches have been developed so far. The complexity of GO makes the derivatization of the oxygenated groups difficult to control. The combination of a nucleophilic epoxide ring opening with the derivatization of the hydroxyl groups through esterification or Williamson reaction was investigated. The conditions were selective and mild, thus preserving the structure of GO. Our strategy of double functionalization holds great potential for different applications in which the derivatization of GO with different molecules is needed, especially in the biomedical field.     

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer

The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born–Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H₂O)₂. It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.     

A finite-element-based coarse-grained model for global protein vibration

Meccanica - Protein mechanical vibrations play a pivotal role in biological activity. In particular, low-frequency (terahertz) modes are related to protein conformational changes, which represent...     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Widened derangements and generalized Laguerre polynomials

The Ramanujan Journal - Let $$D_h$$ , $$E_k$$ and $$F_{\alpha }$$ be sets of size $$h,k,\alpha $$ respectively, with $$k \le h$$ . We define a strongly widened derangement to be a permutation of...     

An Exact Version of the Egorov Theorem for Schrödinger Operators in $$L^{2}({\mathbb {T}})$$ L 2 ( T )

Journal of Fourier Analysis and Applications - We provide an exact version of the Egorov Theorem for a class of Schrödinger operators in $$L^2({\mathbb {T}})$$ , where $${\mathbb {T}}={\mathbb...     

Closed form expressions for Appell polynomials

The Ramanujan Journal - Hafner and Stopple proved a conjecture of Zagier on the asymptotic expansion of a Lambert series involving Ramanujan’s tau function with the main term involving the...     

$$\pi $$π-Formulas and Gray code

In previous papers we introduced a class of polynomials which follow the same recursive formula as the Lucas–Lehmer numbers, studying the distribution of their zeros and remarking that this distribution follows a sequence related to the binary Gray code. It allowed us to give an order for all the zeros of every polynomial \(L_n\). In this paper, the zeros, expressed in terms of nested radicals, are used to obtain two formulas for \(\pi \): the first can be seen as a generalization of the known formula

$$\begin{aligned} \pi =\lim _{n\rightarrow \infty } 2^{n+1}\cdot \sqrt{2-\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{n}}, \end{aligned}$$

related to the smallest positive zero of \(L_n\); the second is an exact formula for \(\pi \) achieved thanks to some identities valid for \(L_n\).